Automatic Data for Applied Railway Management: Passenger
Demand, Service Quality Measurement, and Tactical Planning on
the London Overground Network
by
Michael S Frumin
B.S., Computer Science, Stanford University (2000)
Submitted to the Department of Civil and Environmental Engineering
and the Operations Research Center
in partial fulfillment of the requirements for the degrees of
Master of Science in Transportation
and
Master of Science in Operations Research
at the
Massachusetts Institute of Technology
June 2010
c 2010 Massachusetts Institute of Technology. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Civil and Environmental Engineering
Operations Research Center
May 18, 2010
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nigel H.M. Wilson
Professor of Civil and Environmental Engineering
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jinhua Zhao
Research Scientist of Civil and Environmental Engineering
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dimitris J. Bertsimas
Boeing Professor of Operations Research
Codirector, Operations Research Center
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Daniele Veneziano
Chairman, Departmental Committee for Graduate Students
Automatic Data for Applied Railway Management: Passenger Demand, Service
Quality Measurement, and Tactical Planning on the London Overground
Network
by
Michael S Frumin
Submitted to the Department of Civil and Environmental Engineering
and the Operations Research Center
on May 18, 2010, in partial fulfillment of the requirements for the degrees of
Master of Science in Transportation
and
Master of Science in Operations Research
Abstract
The broad goal of this thesis is to demonstrate the potential positive impacts of applying
automatic data to the management and tactical planning of a modern urban railway. Tactical
planning is taken here to mean the set of transport-specific analyses and decisions required
to manage and improve a railway with time horizons measured in weeks, months, or up to
a year and little or no capital investment requirements.
This thesis develops and tests methods to (i) estimate on-train loads from automatic
measurements of train payload weight, (ii) estimate origin-destination matrices by combining multiple types of automatic data, (iii) study passenger incidence (station arrival) behavior
relative to the published timetable, (iv) characterize service quality in terms of the difference between automatically measured passenger journey times and journey times implied by
the published timetable. It does so using (i) disaggregate journey records from an entryand exit-controlled automatic fare collection system, (ii) payload weight measurements from
“loadweigh” sensors in train suspension systems, and (iii) aggregate passenger volumes from
electronic station gatelines. The methods developed to analyze passenger incidence behavior
and service quality using these data sources include new methodologies that facilitate such
analysis under a wide variety of service conditions and passenger behaviors.
The above methods and data are used to characterize passenger demand and service quality on the rapidly growing, largely circumferential London Overground network in London,
England. A case study documents how a tactical planning intervention on the Overground
network was influenced by the application of these methods, and evaluates the outcomes of
this intervention. The proposed analytical methods are judged to be successful in that they
estimate the desired quantities with sufficient accuracy and are found to make a positive
contribution to the Overground’s tactical planning process.
It is concluded that relative measures of service quality such as the one developed here
can be used in cross-sectional analysis to inform tactical planning activity. However, such
measures are of less utility for longitudinal evaluation of tactical planning interventions when
the basis against which service quality is judged (in this case the timetable) is changed.
Under such circumstances, absolute measures, such as total observed passenger journey
times, should be used as well.
Thesis Supervisor: Nigel H.M. Wilson
Title: Professor of Civil and Environmental Engineering
Thesis Supervisor: Jinhua Zhao
Title: Research Scientist of Civil and Environmental Engineering
Acknowledgments
The research presented in this thesis, indeed the entire course of graduate study which
culminates in this thesis, was made possible by a number of parties whom the author wishes
to thank and acknowledge.
• The Massachusetts Institute of Technology, its Department of Civil and Environmental
Engineering, and the faculty and staff of the Master of Science in Transportation
program for making a home for students interested in the science and practice of
transportation.
• Professor Nigel Wilson and the other leaders of the Transit Research Group for the
opportunity to conduct research into practical problems facing the public transport
providers who make our cities possible.
• Transport for London, and its many staff members in the departments of London
Rail, London Underground, and Fares & Ticketing, for financial support, feedback,
knowledge, and two summers of internship employment.
• Certain railway managers in and around London and New York City, including Oliver
Bratton and Herbert Lambert, for helping ground this thesis in the contemporary needs
and practices of the managers of modern urban railways.
• Dr. Jinhua Zhao, along with Professor Wilson, for supervising the writing of this
thesis.
• The MIT Operations Research Center for allowing the author to dig deeper into many
of the technical and analytical methods applied in the field of transportation and in
this thesis.
• The family, friends, colleagues, and classmates without whom it is difficult to imagine
how the author would be anywhere near where he is today.
5
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Contents
1 Introduction
1.1 Railway Management, Tactical Planning,
1.2 Motivation . . . . . . . . . . . . . . . . .
1.3 Objectives . . . . . . . . . . . . . . . . .
1.4 Research Approach . . . . . . . . . . . .
1.5 Thesis Organization . . . . . . . . . . . .
and Automatic Data
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2 Public Transport in London
2.1 London and the Greater London Authority
2.2 The Public Transport Network . . . . . . .
2.3 Public Transport Fares and Ticketing . . .
2.4 The London Overground Network . . . . .
2.5 Institutional Structures . . . . . . . . . . .
2.6 Investment and Expansion . . . . . . . . .
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3 Data Needs and Sources
3.1 Data Needs . . . . . . . . . . . . . . . . . . . . . . .
3.2 A Synthetic Approach for the London Overground . .
3.3 Data Sources . . . . . . . . . . . . . . . . . . . . . .
3.3.1 The Oyster Smartcard Ticketing System . . .
3.3.2 “Loadweigh” Train Payload Weighing Systems
3.3.3 Station Gatelines . . . . . . . . . . . . . . . .
3.3.4 Manual Passenger Counts . . . . . . . . . . .
3.3.5 Network Representations . . . . . . . . . . . .
3.3.6 Additional Data Sources . . . . . . . . . . . .
4 Calibration of Loadweigh Systems
4.1 Literature Review and Industry Experience . . .
4.2 Model Development . . . . . . . . . . . . . . . .
4.3 Exploratory Analysis . . . . . . . . . . . . . . .
4.4 Calibration Results for the London Overground
4.5 Variability of On-board Loads . . . . . . . . . .
4.6 Conclusions and Recommendations . . . . . . .
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5 Origin-Destination Matrix Estimation
5.1 Public Transport Network Assignment Literature Review
5.1.1 Supply Models . . . . . . . . . . . . . . . . . . .
5.1.2 Paths and Path Choice Models . . . . . . . . . .
5.1.3 Assignment Models . . . . . . . . . . . . . . . . .
5.2 OD Matrix Estimation Literature Review . . . . . . . . .
5.2.1 OD Estimation Example . . . . . . . . . . . . . .
5.2.2 OD Estimation Methods . . . . . . . . . . . . . .
5.2.3 Simulation of OD Estimation Methodologies . . .
5.3 OD Estimation Strategy for the London Overground . .
5.3.1 Assignment Model for the London Overground . .
5.3.2 Information Minimization Matrix Estimation . . .
5.4 Exploratory Analysis of OD Estimation Inputs . . . . . .
5.4.1 Oyster Seed Matrix . . . . . . . . . . . . . . . . .
5.4.2 Link Flows . . . . . . . . . . . . . . . . . . . . .
5.4.3 Gateline Data . . . . . . . . . . . . . . . . . . . .
5.5 OD Estimation Results . . . . . . . . . . . . . . . . . . .
5.5.1 Validation . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Loadweigh Sensitivity Analysis . . . . . . . . . .
5.6 Conclusions and Recommendations . . . . . . . . . . . .
5.6.1 Conclusions . . . . . . . . . . . . . . . . . . . . .
5.6.2 Recommendations . . . . . . . . . . . . . . . . . .
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6 Passenger Incidence Behavior
6.1 Literature Review . . . . . . . . . . . . . . .
6.1.1 Passenger Incidence Behavior . . . .
6.1.2 Schedule-Based Assignment . . . . .
6.2 Methodology . . . . . . . . . . . . . . . . .
6.2.1 Behavioral Assumptions . . . . . . .
6.2.2 Algorithm . . . . . . . . . . . . . . .
6.2.3 Implementation . . . . . . . . . . . .
6.3 Passenger Incidence Behavior on the London
6.3.1 Data . . . . . . . . . . . . . . . . . .
6.3.2 Validation . . . . . . . . . . . . . . .
6.3.3 Results . . . . . . . . . . . . . . . . .
6.4 Conclusions and Recommendations . . . . .
6.4.1 Conclusions . . . . . . . . . . . . . .
6.4.2 Recommendations . . . . . . . . . . .
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Overground
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7 Service Quality Measurement from AFC Data
7.1 Service Delivery and Service Quality Measurement Literature Review
7.1.1 Service Delivery Measurement and The Operator’s Perspective
7.1.2 Service Quality Measurement and The Passenger’s Perspective
7.1.3 Relative Service Quality . . . . . . . . . . . . . . . . . . . . .
7.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
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7.2
7.3
7.4
7.5
Analytical Framework and Assumptions . . . . . . . . . . . . . . . . . . . .
7.2.1 Journey Time Components and Standards . . . . . . . . . . . . . . .
7.2.2 Passenger Incidence and Behavioral Assumptions . . . . . . . . . . .
7.2.3 Framework Intuitions . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Unified Unbiased Estimator for Aggregate Excess Journey Time . . . . . .
7.3.1 Framework for Aggregate EJT . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Equivalence of Random and Scheduled Incidence Assumptions for Aggregate EJT of Random Incidence Passengers . . . . . . . . . . . . .
7.3.3 Blended Passenger Incidence Behavior . . . . . . . . . . . . . . . . .
7.3.4 Extension to a Heterogeneous Rail Network with Interchanges . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1 Application Considerations . . . . . . . . . . . . . . . . . . . . . . . .
7.4.2 Negative EJT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.3 EJT and Longitudinal Analysis . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Oyster-Based Excess Journey Time on the London Overground
8.1 Excess Journey Time Methodology for the London Overground . . .
8.2 Graphical Validation . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 Excess Journey Time on the London Overground . . . . . .
8.3.2 Comparison with Existing Performance Metrics . . . . . . .
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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10 Final Remarks
10.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.1 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.2 Applications of Automatic Data to Tactical Planning . . . . . . . .
10.1.3 Methodological Contributions . . . . . . . . . . . . . . . . . . . . .
10.2 Recommendations for Data Collection on the London Overground Network
10.3 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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9 Tactical Planning Case Study on the London Overground
9.1 The North London Line: Spring 2008 . . . . . . . . . . . . .
9.1.1 The Service Plan . . . . . . . . . . . . . . . . . . . .
9.1.2 Passenger Demand . . . . . . . . . . . . . . . . . . .
9.1.3 Operating Performance: Service Delivery and Quality
9.2 Tactical Planning Intervention: The Case for Even Intervals
9.2.1 “3 + 3” Service on the North London Line . . . . . .
9.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.1 Evaluation Data . . . . . . . . . . . . . . . . . . . .
9.3.2 Evaluation Results . . . . . . . . . . . . . . . . . . .
9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A London Overground Station Information and Abbreviations
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B London Overground Line and Segment Abbreviations
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C Schematic Map of TfL Rail Services
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D Assignment Model Algorithm for Operator Aggregation
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E Terms and Abbreviations
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10
List of Figures
1-1 Conceptual diagram of tactical planning hierarchy. . . . . . . . . . . . . . . .
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2-1 High level institutional structure for public transport service provision in London 23
2-2 Map of the London Overground network, with other rail services . . . . . . . 26
4-1 Cumulative distribution of London Overground loadweigh measurements . .
4-2 Loadweigh weight vs. time of day (random 10% sample) . . . . . . . . . . .
4-3 Loadweigh weight vs. time of day for peak load point of London Overground
network (Canonbury to Highbury & Islington) . . . . . . . . . . . . . . . . .
4-4 Loadweigh weight vs. manual count data . . . . . . . . . . . . . . . . . . . .
4-5 Residual vs. manual count for all data (unit segmented) and terminals-only
(pooled) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-6 Loadweigh weight vs. time of day for peak load point data . . . . . . . . . .
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Example of line-based representation of public transport network . . . . . .
Example OD estimation problem . . . . . . . . . . . . . . . . . . . . . . . .
Waiting time as a function of headway . . . . . . . . . . . . . . . . . . . . .
Illustration of network augmentation . . . . . . . . . . . . . . . . . . . . . .
Sensitivity of London Overground Oyster-only competitive market size and
assigned trips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distribution of non-zero OD flows in Oyster AM Peak seed OD matrix . . .
Counted and assigned Oyster link flows for AM Peak, March 2009 . . . . . .
Oyster and gateline entry and exit counts at stations exclusive to the London
Overground with recorded gateline data, March 2009 weekday AM Peak periods
Estimated OD flow vs OD flow from the Oyster seed matrix, clamped to
London Overground network . . . . . . . . . . . . . . . . . . . . . . . . . . .
Estimated OD flow vs OD flow from the Oyster seed matrix, by London
Overground Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Smoothed densities of OD validation measures under simulated loadweigh error
45
45
48
49
75
79
80
81
83
83
89
6-1 Distributions of passenger incidence for different levels of reliability of departure time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6-2 Illustration of run-based supply model . . . . . . . . . . . . . . . . . . . . . 101
6-3 Distributions of passenger incidence headways, by line and time period . . . 108
6-4 Distributions of passenger incidence, by London Overground line and time
period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
11
6-5 Mean scheduled passenger waiting time by London Overground line and time
period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7-1 Example Time-Distance Graph . . . . . . . . . . . . . . . . . . . . . . . . .
7-2 Example probability density function of incidence time for scheduled incidence
passengers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-3 Example probability density function of incidence time for random incidence
passengers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-4 Example probability density function of incidence time for blended random
and scheduled incidence passengers . . . . . . . . . . . . . . . . . . . . . . .
8-1 Time-distance illustration of EJT estimation for a passenger
to Camden Road . . . . . . . . . . . . . . . . . . . . . . . .
8-2 Time-distance plot of timetable and observed Oyster exits
travel on the North London Line on 3 April, 2008 . . . . . .
8-3 Distributions of EJT in AM Peak periods . . . . . . . . . . .
8-4 Total EJT, by line and time period . . . . . . . . . . . . . .
8-5 Mean EJT, by line and time period . . . . . . . . . . . . . .
8-6 Daily Mean EJT . . . . . . . . . . . . . . . . . . . . . . . .
8-7 Total EJT on the NLL, by time period and direction . . . .
8-8 Mean EJT on the NLL, by time period and direction . . . .
8-9 Total EJT by scheduled service, westbound . . . . . . . . . .
8-10 Mean EJT by scheduled service, westbound . . . . . . . . .
8-11 EJT and PPM, by line . . . . . . . . . . . . . . . . . . . . .
8-12 Mean EJT vs PPM, for NLL . . . . . . . . . . . . . . . . . .
9-1
9-2
9-3
9-4
9-5
9-6
9-7
from Stratford
. . . . . . . . .
for westbound
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
London Overground Spring 2008 AM Peak service patterns and frequencies
North London Line Spring 2008 AM Peak timetable . . . . . . . . . . . . .
NLL AM Peak load profile . . . . . . . . . . . . . . . . . . . . . . . . . . .
AM Peak passenger incidence on NLL and GOB . . . . . . . . . . . . . . .
London Overground “3 + 3” service patterns and frequencies . . . . . . . .
North London Line “3 + 3” timetable . . . . . . . . . . . . . . . . . . . . .
Total EJT by scheduled service, westbound, after “3 + 3” implementation
.
.
.
.
.
.
.
125
128
129
134
142
145
147
148
148
150
150
151
152
152
153
154
159
159
161
162
168
168
173
C-1 Schematic map of TfL rail services . . . . . . . . . . . . . . . . . . . . . . . 194
12
List of Tables
2-1 Size and patronage of the public transport networks in London . . . . . . . .
2-2 Primary London Overground service patterns . . . . . . . . . . . . . . . . .
22
25
3-1 Current and proposed data collection strategies for the London Overground .
34
4-1 Loadweigh calibration results . . . . . . . . . . . . . . . . . . . . . . . . . .
47
5-1
5-2
5-3
5-4
71
80
82
Labels and weights for identification of alternative paths . . . . . . . . . . .
Aggregate ratio of assigned Oyster flow to counted flow, by line . . . . . . .
Summary statistics for London Overground estimated AM Peak OD matrix .
Selected OD flows with large estimated values and large relative and/or absolute expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-5 Comparison of estimated and counted boardings and alightings . . . . . . . .
5-6 Line and line segment level validation on counted AM Peak boardings for
RailPlan (2008) and Oyster-based OD estimates . . . . . . . . . . . . . . . .
5-7 Average values of validation measures for OD estimation under simulated
loadweigh error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-1
9-2
9-3
9-4
Segment level NLL AM Peak origin-destination matrix . . . . . . . . . . . .
NLL and WLL service under the Spring 2008 and the “3+3” tactical plans .
Volumes of Oyster data in evaluation study periods . . . . . . . . . . . . . .
PPM and passenger journey time results and comparisons for “3 + 3” implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
85
86
88
160
167
171
171
A-1 London Overground stations . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B-1 London Overground lines and line segments . . . . . . . . . . . . . . . . . . 191
13
14
Chapter 1
Introduction
This thesis develops and applies methods for using automatic data to characterize urban
railway passenger demand and service quality, primarily for the purposes of supporting
railway managers in the process of tactical planning. In the context of this thesis, tactical
planning 1 is taken to mean the set of transport-specific analyses and decisions required to
manage and improve a railway with time horizons measured in weeks, months, or up to a
year and little or no capital investment requirements.
This thesis proceeds in three principle endeavors. First, it develops and applies methods
to characterize passenger demand spatially, temporally, and behaviorally. Second, it develops
and applies a method to characterize service quality in terms of the difference between actual
passenger journey times and journey times implied by the published timetable. Finally, it
documents how a tactical planning intervention was influenced by the application of these
methods, and evaluates the outcomes of this intervention. The broad goal of this thesis is to
demonstrate the potential positive impacts of applying automatic data to the management
and tactical planning of a modern urban railway.
The automatic data central to this thesis are (i) disaggregate passenger journey transactions from an entry- and exit-controlled automatic fare collection (AFC) system, (ii) payload
weight measurements from sensors in train suspension systems, and (iii) aggregate passenger
volumes from electronic station gatelines. In some cases, a single type of data is sufficient
to derive the desired results. More often than not, it is necessary to combine multiple types
of automatic data with each other and with reference data such as network representations
and public timetables.
The research presented in this thesis has been developed commensurate with the analytical needs of the managers of the rapidly growing, largely circumferential London Overground
network in London, England. The methods developed in this thesis are each applied to data
from this railway, both as a test of the method and for the sake of analyzing the railway
and its passengers per se. This thesis includes a case study which demonstrates the use of
these methods to support and evaluate a tactical planning effort on the core portion of the
Overground network. While the work in this thesis is motivated primarily by problems facing
the managers and passengers of the Overground, the methods it develops should generalize
well to other contexts where similar automatic data are available.
1
What is referred to here as “tactical planning” is also commonly referred to as “service planning.”
15
Section 1.1 of this chapter describes selected aspects of railway management, including
tactical planning, and the relevance of automatic data thereto. Section 1.2 describes the
motivations for this thesis, and Section 1.3 describes its specific objectives. Section 1.4 gives
an overview of the approach for the research described in this thesis. Section 1.5 describes
the organization of the balance of this document.
1.1
Railway Management, Tactical Planning, and Automatic Data
Railways can be complex and multi-faceted organizations, with certain management functions similar to any large enterprise. The aspect of railway management with which this
thesis is primarily concerned is tactical planning, as defined in the introduction to this chapter. The decision processes that make up tactical planning include the following, as per
Wilson (2008), and described in detail by Ceder (2007) and Vuchic (2005). In this type of
planning, demand levels are often considered to be constant.
• Network Design – route design over a fixed infrastructure network.
• Frequency Setting – determination of service frequencies for each route, for different
service periods (e.g. by time of day and day of week).
• Timetable Development – creation of a specific timetable, including running times, to
provide a certain frequency of service on a set of routes.
• Vehicle Scheduling – scheduling of vehicles to cover all trips in the timetable.
• Crew Scheduling – scheduling of crews to staff all vehicles.
These decisions are often but not always described and implemented hierarchically, as shown
in Figure 1-1.
At the top of the hierarchy, starting with network design, decisions tend to be infrequent,
dominated by service considerations, and driven by judgment and manual analysis. Moving
down the hierarchy, towards crew scheduling, decisions are more frequent, dominated by
cost concerns, and can be computer driven by automatic tools such as optimization-based
scheduling software. Tactical planning thus encompasses numerous types of analyses and
decisions, only a few of which are treated explicitly in this work, more of which can benefit
from the methods developed here, and many of which could benefit from the use of automatic
data in general.
The decisions made on a day-to-day real-time basis to implement a given tactical plan can
be described as service control. Studied by Carrel (2009) for high frequency urban railway
services, these decisions include the assignment of physical vehicles to vehicle schedules, the
assignment of drivers to vehicles, and various types of modifications to these schedules and to
the timetable to account for disruptions and delays. Froloff et al. (1989) study and describe
this topic for urban bus, rather than railway, services.
Decisions made with much longer time horizons or demanding substantial capital investment can be referred to as strategic planning. This type of planning is more akin to overall
16
Infrequent
Decisions
Service
Considerations
Dominate
Judgement &
Manual Analysis
Dominate
Network Design
Frequency Setting
Timetable Development
Vehicle Scheduling
Crew Scheduling
Frequent
Decisions
Cost
Considerations
Dominate
Adopted from Wilson (2008)
Computer-Based
Analysis Dominates
Figure 1-1: Conceptual diagram of tactical planning hierarchy.
transport planning, as described by Meyer and Miller (2001). It typically considers substantial changes to land use, economic development, and overall levels of demand as well as shifts
of demand between different transport modes (e.g. public vs. private transport).
Information Technologies and Automatic Data
At a major urban railway by which the author has been employed, staff from the lowest to
the highest levels refer to the operation of the railway as “making service.” This choice of
words attests to the fundamental nature of railway operation as an industrial production
process. Like other service and manufacturing production processes, railways are heavily
dependent on technology. For example, the capacity of a railway is largely determined by
the design of its propulsion and signaling systems (Kittelson & Associates, Inc et al., 2003b).
In railways, as in other technology-driven industries, information technology (IT) has
played an increasingly larger role over time. Traditionally, railways have invested heavily
in IT systems for core production and real-time management functions such as signaling,
dispatching, vehicle operation, and service control (Vuchic, 2007), as well as key auxiliary
functions such as fare collection (Multisystems, Inc et al., 2003) and passenger information
systems (Multisystems, 2003). By their very nature, these IT systems serve to automatically
create, transmit, manipulate, display, and store electronic data. This thesis is not about the
impact of these kinds of systems per se on railway operations. Rather, this thesis is about
how the data produced and stored by these various IT systems can and should be used in
analytical management functions, specifically tactical planning. It is hoped that the methods
developed in this thesis find application in other contexts as well.
1.2
Motivation
Most broadly, this thesis is motivated by the hypothesis that the managers of railways and
other public transport services have much to gain from the use of automatic data sources for
17
tactical planning. These data sources represent a significant and often unused analytical asset
that can be highly leveraged to help improve service and decrease costs in many different
contexts.
On a more narrow level, this work is motivated by a need in the railway industry for
methods to make more effective analytical use of available automatic data to understand
passenger demand and service quality. In that sense, it is motivated by needs of managers of
railways in London and around the world facing similar tactical planning challenges as the
managers of the London Overground. One such need is to better understand and measure
passenger behavior and service quality, and to understand how specific tactical planning
interventions affect certain aspects of the passenger experience.
On the most narrow level, the work in this thesis is motivated by the immediate and
ongoing analytical needs of the mangers of the Overground. Foremost among their needs
are the ability to measure passenger loads on individual scheduled services, to estimate total
passenger boardings at individual stations, and to understand passenger travel patterns
at the level of origin-destination (OD) flows. Currently, these needs are met primarily
through manual data collection efforts, and so are impossible to satisfy cost-effectively at
desired frequencies or sample sizes. An additional contemporaneous need of the Overground’s
managers is to understand the overall impact on passengers of the recent tactical planning
exercise on the core portion of the Overground network.
1.3
Objectives
The most broad-based objective of this thesis is to investigate the use of automatic data
in the tactical planning of urban railways. This should be accomplished by demonstrating
that the use of automatic data through application of the methods developed here in fact
contributed to measurable improvement in the service quality of the London Overground.
A more specific objective is to provide to the Overground’s managers insights into passenger demand and service quality that are relevant to tactical planning but are inaccessible
without automatic data. In other words, to develop methods that take advantage of the richness of available automatic data to achieve the following previously unavailable analytical
results.
• Understand the relationship between the published timetable and passenger arrival
behavior at stations.
• Measure railway service quality as experienced by passengers in terms of the difference
between actual journey times and journey times implied by the published timetable.
• Document the recent tactical planning exercise on the core portion of the Overground
network, including the application of the above results to this process.
• Evaluate the outcomes of the resulting tactical planning intervention. This evaluation
should be primarily from the perspective of passengers, but should also consider the
experience and process of operators and managers.
18
An additional objective of this thesis is to develop a prototype of a data collection scheme
with associated methods to meet the immediate and ongoing analytical and tactical planning
needs of the mangers of the Overground. This scheme should maximize the use of automatic
data and minimize cost, primarily through minimizing the need for manually collected data.
It should improve the quality, breadth, and timeliness of its outputs, with the goal of supporting continued improvement in Overground services through improved tactical planning.
The specific objectives are as follows.
• Understand the error associated with train payload weighing systems, and calibrate
them for use in directly measuring passenger loads on trains.
• Develop and test a method to estimate station-to-station origin destination flows on
the Overground at the time-period level, and use this result to estimate total boardings
at the station level.
1.4
Research Approach
The overall approach to this research is pragmatic and applied. Since the goal is to address
certain issues faced by the managers of urban railways, this thesis draws on models and
techniques from existing literature whenever possible and proposes new methods only when
necessary. Mathematical models and statistical techniques, when necessary, are selected to
be as simple as possible, but no simpler.
To achieve the stated objectives, the research in this thesis will do the following.
• Calibrate loadweigh systems using a linear regression of a sample of loadweigh measurements from the London Overground against paired manual on-board passenger counts.
Use the results of this regression to understand the error associated with loadweigh
data.
• Estimate station-to-station passenger demand for the Overground in the AM Peak
period from multiple sources of data using network and mathematical models. The
data sources used are aggregate Oyster journey data, automatic gateline entry counts,
and a complete set of manual on-board passenger counts (standing in for loadweigh
data). Test the sensitivity of this estimate to randomness in the on-board counts when
estimated from loadweigh data.
• Assign individual Overground passenger journeys with specific scheduled services in
the published timetable. This assignment depends on network models and algorithms
applied to each Oyster journey and its associated origin, destination, and time of entry
time into the system.
• Using that assignment, analyze passenger arrival behavior at stations by comparing
the entry times of passenger journeys with respective scheduled departure times.
• Also using that assignment, measure service quality in terms of the difference between
actual passenger journey times estimated from disaggregate Oyster data and scheduled
19
passenger journey times from the published timetable. Aggregate these values along a
variety of dimensions to assess service quality on the Overground.
• Document the recent tactical planning exercise on the North London Line of the Overground network, including its use of these and other results.
• Evaluate the outcomes of implementing the new tactical plan resulting from this exercise, primarily in terms of its effects on passengers.
• Use this case study as means to assess the applicability of the methods developed in
this thesis for improved tactical planning using automatic data.
1.5
Thesis Organization
This thesis is organized into 10 chapters, including this one. Chapter 2 provides background
information on the London Overground and the broader network of public transport services in London, England. Chapter 3 describes the various data sources available to the
Overground, automatic or otherwise, how they are currently used by the Overground, and
how they could be used. Chapter 4 develops and applies a method for calibrating train
payload weighing systems to measure passenger loads. Chapter 5 develops and applies a
method, tailored to the circumstances of the Overground, to estimate time period level
origin-destination matrices from multiple data sources. Chapter 6 develops and applies a
method to analyze passenger arrival behavior at stations. Chapter 7 develops and justifies
a unified method to use actual passenger journey times to measure service quality relative
to published timetables. Chapter 8 applies that method to the Overground, validates it,
and compares it to existing performance measurements. Chapter 9 presents a case study on
the use of these methods to inform and evaluate a recent tactical planning exercise on the
Overground. Chapter 10 offers some final remarks, including conclusions, recommendations,
and areas for future research.
This thesis covers a range of topics but is intended, to a certain degree, to be consumable
in a piecemeal fashion. To that end, it groups literature review, methodologies, and results
topically into single chapters or consecutive sets of chapters. This applies most directly to
Chapter 4, Chapter 5, Chapter 6, and the combination of Chapters 7 through 9.
20
Chapter 2
Public Transport in London
This chapter provides a broad background of the city of London and its public transport
network, including the London Overground. Section 2.1 gives a brief introduction to the
city of London. Section 2.2 describes some of the key elements of London’s public transport
network. Section 2.3 describes the fare structure and ticketing systems of that network.
Section 2.4 describes the Overground network from a transport perspective. Section 2.5
describes the institutional structure of the Overground. Finally, Section 2.6 describes some
of the key elements of the Overground’s investment program.
2.1
London and the Greater London Authority
London, a city of approximately 7.5 million inhabitants covering 1,572 square kilometers,
is located in the southeast of the United Kingdom, of which it is the capital (Government
Offices, 2010). The Greater London Authority (GLA), created by a 1999 act of the British
parliament, governs London at a regional and strategic level. The primary executive of the
GLA is the popularly elected Mayor of London (Greater London Authority, 2010a). The
Mayor has wide powers over the city’s transportation agency, Transport for London (TfL),
including setting its strategy and budget and appointing its board. TfL manages most facets
of the transport system in London, including roads, the congestion charge, and local public
transport (Greater London Authority, 2010b). It has an ambitious investment program of
over £35 billion from 2009 through 2018 (Transport for London, 2009c).
2.2
The Public Transport Network
London has a world class public transport system, serving an estimated 12 million passenger
“journey stages” on an average in 2007, representing a growth of almost 60% since 1991
(Transport for London, 2009f). Table 2-1 shows the size (in stops or stations) and annual
ridership of the largest components of this system, described in further detail in the following
paragraphs.
London’s more than 8,000 local buses ply a network serving almost 19,000 stops on over
700 routes, carrying an estimated 2 billion yearly passengers (Transport for London, 2009d).
The London Underground (LU), a world-famous metro system with routes going back 150
21
Network
London Buses
London Underground (LU)
Docklands Light Railway (DLR)
London Overground (LO)
National Rail (NR) in London
Number of
Stops or Stations
19,000
402
40
56
318
Approximate Annual
Ridership (millions)
2,000
1,000
70
33
883
Table 2-1: Size and patronage of the public transport networks in London
years, serves an estimated billion passengers annually on a 402 kilometer network of 270
stations on 11 lines (Transport for London, 2010c). The Docklands Light Railway (DLR),
which opened in 1987, serves an estimated 70 million yearly passengers on a 40-station
network in parts of East London and the newer Canary Wharf financial district (Transport
for London, 2009b). The London Overground, an above-ground urban railway re-christened
in 2007, serves an estimated 33.4 million passengers annually over a largely circumferential
107 kilometer network of 56 stations on four lines (Smales, 2009). It is the focus of the
research in this thesis and will be described in further detail in the following sections.
The United Kingdom’s system of regional and inter-city railways, referred to as National
Rail (NR), serves London’s commuters and visitors at 318 stations within Greater London
(Office of Rail Regulation, 2009) and connects the capital with the rest of the country. The
National Rail network serves an estimated 833 million passengers annually in London and
the southeast of England, and an estimated 1.2 billion passengers across the entire country
(Office of Rail Regulation, 2008). National Rail services are operated by twenty-nine regional
Train Operating Companies (TOCs) across the entire country, most of which serve London
either in a commuter or long distance capacity (National Rail, 2010). Each TOC operates
according to a competitively bid franchise agreement, let by the national Department for
Transport (DfT). This is of particular relevance to this thesis because of the Overground’s
unique relationship, described in the following sections, to both TfL and the National Rail
system.
Broadly speaking, London’s public transport is very well integrated. Interchanges between the different rail services are available at more or less all possible opportunities (Transport for London, 2010e), and most if not all bus routes connect to the rail network at one
or more points.
TfL is responsible for all the services described in this section other than those operated by
National Rail TOCs. Only the London Underground is operated directly by TfL employees.
All other bus and railway services are provided by competitively bid operational concessions
let by TfL. In all of these concessions, TfL holds all of the revenue risk in some concessions and
almost all of the revenue risk in others. TfL itself is organized into modal units and a central
corporate finance and planning group. The largest modal units are eponymous London
Underground, Surface, managing roads and Buses, and London Rail, which manages TfL’s
other rail services (including the Overground and the DLR) as well as acting as TfL’s liaison
to the National Rail network and the TOCs. Figure 2-1 provides a high level organization
chart illustrating these relationships for providing public transport service (this chart does
not describe the ownership and responsibility for infrastructure).
22
Mayor of
London
National
Government
Transport for
London (TfL)
Department for
Transport (DfT)
TOC
TOC
…
London
Underground
TOC
National Rail
Train Operating Companies
(TOCs)
London
Rail
Ownership/Subsidiary
Relationship
LOROL
Contract/Concession
Relationship
DLR
Concession
London
Buses
…
Bus
Concessions
Figure 2-1: High level institutional structure for public transport service provision in London
2.3
Public Transport Fares and Ticketing
The fare structure for rail services in London is integrated, with the primary exception that
neither transfers between buses nor between bus and rail are free for passengers lacking
unlimited-use passes. Rail travel in London, be it by TfL or National Rail services, is
generally priced on a zonal basis, where the zones are oriented concentrically around Central
London (see the map in Appendix C). The price of a journey depends not only on the starting
and ending zones, but also on which zones that journey has passed through – trips through
lower zones (i.e. through more central parts of London) cost more. Rail fares also have
a temporal component, with a premium charged for travel during peak commuting hours.
Interchanges between rail services are free in some (e.g. between London Underground lines),
but not all cases (e.g. between some National Rail and Underground services). Bus travel is
priced on a per-boarding basis, with no discount for interchanging between buses or between
bus and rail (Transport for London, 2010b).
Unlimited-use passes, called travelcards or season tickets, are also available for different
zonal combinations (e.g. zones 1-2, 1-3, 2-4, etc) and different lengths of time (e.g. one day,
seven days, 30 days, one year). Travelcards cover all public transport travel – all TfL
and National Rail services – within the selected zones. The price of a travelcard of course
23
depends on the zonal and temporal coverage, with the potential discount offered to the
purchaser increasing with the temporal span of the ticket (Transport for London, 2010a).
London’s public transport fare structure includes a host of other discount schemes, including
bus-only passes, concessions for students and the elderly, and point-to-point season tickets
on National Rail.
Public transport fares in London are clearly complex, but the application of ticketing
technologies has progressively simplified the details that passengers must understand and
choices they must make. In particular, the introduction and evolution of the Oyster smartcard ticketing system has made certain aspects of public transport ticketing in London much
more efficient for passengers and for operators. A passenger can add monetary value to his
or her Oyster card in bulk and then simply “Pay As You Go” (PAYG) by validating the
card when entering and exiting the transport network (Transport for London, 2009e). The
Oyster system deducts the correct amount of money from the passenger’s card for each journey, including in such complicated cases as “Out-of-Station Interchanges” (OSIs) when the
journey requires exiting and re-entering the transport network to transfer between services
at certain nearby but unconnected stations. This saves passengers without travelcards the
effort of having to purchase individual tickets for each journey, and saves operators the effort
of having to sell them. To incentivize the use of Oyster cards, TfL has imposed a significant
price penalty for the purchase of single tickets (Hong, 2002).
Oyster cards also support the purchase and use of travelcards, which TfL no longer offers
on traditional magnetic-stripe media. TfL no longer offers single-day travelcards either,
instead offering Oyster PAYG users daily “price capping” or “best value.” Under this scheme,
the Oyster system calculates the price of the single-day travelcard or pass that would have
been necessary to accommodate all of the user’s rail and bus travel on that day, and stops
deducting from their Oyster card’s balance once that amount has been reached (Transport
for London, 2009e).
Traditionally, neither PAYG nor daily capping were available for most of the National
Rail network. In January, 2010, this changed with the negotiation and implementation of
the Oyster eXtension to National Rail (OXNR) project, which extended the Oyster system
to almost all National Rail stations within Greater London (Transport for London, 2010b).
However, the various National Rail TOCs do not generally retail Oyster products (neither
cards nor PAYG value nor travelcards) at their stations, so many National Rail passengers in
London still use magnetic-stripe tickets, chiefly travelcards, to pay for their journeys (Chan,
2007).
Since its introduction in 2003, the Oyster system has grown to become the dominant fare
media for TfL services, processing over 10 million transactions daily. Over 6 million cards are
in regular use, and over 80% of all bus and London Underground journeys were made using
Oyster in 2009 (Transport for London, 2009e). That said, there are circumstances where
Oyster has significantly less penetration on the TfL network. This is most often the case at
places and times where large volumes of National Rail commuters or visitors interchange to
or from TfL services, for example at large intermodal facilities (e.g. Victoria station) during
peak commuting hours (Chan, 2007). This must be considered when using the Oyster system
as a source of data on passenger journeys.
24
2.4
The London Overground Network
Figure 2-2 shows a map of the London Overground network (with other railways) as of January, 2009. A schematic map, with detailed interchange information is shown in Appendix
C. The Overground network is for the most part circumferential, primarily orbiting London
to the North and West, with only a single station (Euston) in fare zone 1 and the majority
of stations in zones 2 and 3. The Overground is very much part of the overall integrated
network of TfL and National Rail services, with 19 of its stations offering interchanges to
London Underground or DLR services and 13 of its stations offering interchanges to National
Rail (24 stations offer at least one interchange). Key Overground stations, such as Stratford,
Clapham Junction, and Euston, are major intermodal terminals or interchange points. In
2010, the Overground is running 407 scheduled weekday trips with 27 units of rolling stock
(i.e. trains) (Brimbacombe, 2010).
Services on the Overground are for the most part divided into four different lines (i.e. service
patterns) as described in Table 2-2. The core of this network is the North London Line (NLL)
which runs 28 kilometers between Stratford in the northeast of London and Richmond in
the southwest, connecting to every other Overground service and numerous other TfL and
National Rail services along the way. It is by far the busiest Overground line, with the
most frequent service and an estimated 58% of all Overground boardings (Smales, 2010).
The NLL runs four (end-to-end) trains per hour (tph) over most of the day, with some segments receiving six tph during the peak periods. Of the twenty-three stations on the NLL,
seventeen are served only by the Overground.
The other Overground lines run at lower frequencies of three tph during the peak periods
and two to three tph during other periods. In the case of the Gospel Oak to Barking
(GOB) line, which is the only service available at nine of its twelve stations, these lower
frequencies are the result of relatively low passenger demand. The other two Overground
lines run at these low frequencies because of competition from other services. The fivestation West London Line (WLL) shares all but one station (Willesden Junction, its northern
Terminus) with another National Rail TOC. The much longer nineteen-station Watford DC
Line runs interavailably1 for ten consecutive stations in the middle of its route with the
London Underground’s Bakerloo line, and National Rail express services run much more
quickly from some of its northernmost stations to its southern Central London terminus
(Euston). During peak periods, select Overground services run special patterns described in
detail in Chapter 9.
Service Pattern (Line)
Code
Primary Terminals
North London Line
Gospel Oak to Barking Line
Watford DC Line
West London Line
NLL
GOB
WAT
WLL
Stratford ⇔ Richmond
Gospel Oak ⇔ Barking
Watford Junction ⇔ London Euston
Clapham Junction ⇔ Willesden Junction
Frequency
(Peak tph)
4-6
3
3
2-3
Table 2-2: Primary London Overground service patterns
1
“Interavailability” describes the situation where two (or more) services are available on the same platform
and travel to some (or all) of the same stations down the line.
25
Overground lines are denoted in orange (dashes indicate lines in planning or under construction), Underground (and DLR) in red, and National Rail
in blue
Figure 2-2: Map of the London Overground network, with other rail services
26
On November 11, 2007, overall management and revenue responsibility for this set of
services was transferred to TfL from the Silverlink TOC which held the prior National Rail
franchise. At that time, the network was re-branded as the Overground and became fully
Oyster-enabled. TfL’s goals in absorbing the Overground were to improve service standards
(including station safety and staffing) and to deliver the investments and expansions described in Section 2.6 (Transport for London, 2007a). TfL contracted the operation of the
Overground to a private concessionaire, creating the fairly unique institutional structure
described in the following section.
2.5
Institutional Structures
London Rail, also referred to legally as Rail for London (RfL), delivers London Overground
services through a concession contract with the private operator London Overground Rail
Operations Limited (LOROL). London Rail plays other non-operational roles in the management of the Overground network, including
• planning and specifying service levels, including frequencies and train lengths,
• planning and funding major investments (i.e. strategic planning),
• delivering those investments through contracts with infrastructure and rolling stock
providers,
• monitoring and forecasting revenues and demand,
• working with LOROL to respond to changing conditions on the network,
• and communicating with the riding public and other stakeholders.
In this sense, tactical planning for the Overground is a shared responsibility between London
Rail and LOROL.
LOROL is a joint venture between two world-class private (but largely state-owned)
railway operators – MTR Corporation of Hong Kong and Deutsche Bahn AG of Germany
(LOROL, 2010). Among LOROL’s contracted responsibilities are to
• develop public and working timetables to meet certain service level commitments,
• hire and train station staff, train crews, and service controllers,
• make and manage train and station service on a daily basis,
• conduct light maintenance on stations and vehicles,
• gather information on passenger demand,
• cooperate with infrastructure upgrades and expansions
27
(Rail for London Limited and MTR Laing Metro Limited, 2007).
Note that LOROL is not responsible for maintaining and operating the infrastructure
(i.e. tracks, switches, and signals) on which it runs. This is because the Overground operates
on infrastructure owned, maintained, and operated by Network Rail, the public benefit corporation responsible for the National Rail network infrastructure. LOROL operates within a
well defined institutional, financial, and political framework that structures the relationships
between the infrastructure owner (i.e. Network Rail), operators (i.e. TOCs), and sponsors
(i.e. DfT and TfL).
An in-depth discussion of this framework is beyond the scope of this thesis. It is sufficient
to say that the institutional structure described here places the Overground in a unique
context in London. On the one hand it is the only National Rail franchise let by other than
DfT and with essentially no revenue stake for the franchisee. On the other hand, it is the
only TfL service that is run by a private operator on infrastructure owned neither by TfL
nor by the operator. One implication of this arrangement, further discussed in Chapter 8, is
that the performance and incentive regime for the Overground is rooted in the regime used
across the National Rail network.
2.6
Investment and Expansion
The London Overground network is currently the subject of over £1.5 billion of investment
in extensions, infrastructure upgrades, and new rolling stock. As a result, it is set to grow
significantly over the next several years in terms of network size, service density, and passenger demand. A longer-term goal of these investments is to support access to Stratford,
the site of the 2012 Summer Olympic Games (Transport for London, 2007b, 2009c). Among
the most significant investments in the Overground network are:
East London Line Extension (ELLX) – Opening in stages starting in the spring of
2010, this project will rehabilitate and extend what was the London Underground
East London Line and add it to the Overground network. Shown in Figure 2-2, the
old East London Line is being extended to the north and to the south, and will enter
service with 12 tph on the trunk portion. North of Shoreditch High Street station, new
infrastructure will bring rail service for the first time to some parts of inner East London. South of New Cross Gate station, a connection to the National Rail network will
improve access from South London to the TfL network and to parts of East London.
Some service on this line will eventually terminate at Highbury & Islington and connect
directly to the North London Line. This project is projected to serve an estimated 33.2
million passengers in 2011 (AECOM, 2006), effectively doubling Overground ridership.
North London Railway Infrastructure Package (NLRIP) – To be completed in advance of the 2012 Olympics, this project will upgrade track, switches, and signals,
primarily on the core portion of the North London Line between Stratford and Willesden Junction. These are set to support frequencies of up to 12 tph on the North
London Line.
East London Line Phase 2b – Through a number of small connections and reconfigurations, this project will connect the Overground between Crystal Palace (on the ELL)
28
to Clapham Junction (on the WLL) through South London. Set to open in 2012, it
will complete the Overground’s orbital route structure.
New Rolling Stock – By 2012, the entire planned Overground fleet of 216 rail cars, in
three-car and four-car trains, will be new Class 378 vehicles from Bombardier Transportation. This fleet has wider doors and longitudinal seating to improve the capacity
and performance under heavy demand, and passenger amenities such as air conditioning and improved passenger information systems. An important feature of this fleet
in the context of this thesis is that its computerized braking systems will measure and
report train payload weights for the sake of estimating passenger loads.
This Overground investment program is just one part of the much larger and very ambitious TfL investment program, which includes major upgrades to the London Underground
and DLR as well as the new £16 billion Crossrail project (Transport for London, 2009c).
29
30
Chapter 3
Data Needs and Sources
This chapter proposes a new approach to data collection and demand estimation for the
London Overground network. The new approach is designed to minimize cost and maximize
the use of automatic data sources while satisfying the various reporting and analytical requirements of the network’s public owner and private operator. It is designed to improve
the quality, breadth, and timeliness of its outputs, with the goal of supporting continued
improvement in Overground services through improved tactical planning. Broadly speaking,
the goal of such a strategy is to change data collection from an infrequent, expensive, manual
process to a frequent, cost-effective, automatic one.
Section 3.1 describes the immediate data needs of the managers and planners of the
Overground and how those needs are currently met. Section 3.2 outlines an approach to
meet these specific needs using a range of automatic data sources. Section 3.3 describes in
detail each data source, with respective limitations, that will be used to support the proposed
approach and other methods and analyses developed later in this thesis.
3.1
Data Needs
While TfL’s and LOROL’s interests are generally aligned, they have different analytical data
needs as a consequence of their different responsibilities. The primary quantities of interest to
TfL and/or LOROL analysts and tactical planners are the following (Smales, 2009; Bratton,
2009).
• Average loads on individual scheduled services (i.e. timetabled trips) between all consecutive stations.
• Average total boardings, by station, at the time period (e.g. AM Peak) level.
• Average origin-destination flows between all pairs of Overground stations at the time
period level.
TfL’s concession contract with the Overground’s private operator requires twice-yearly
passenger counts (Rail for London Limited and MTR Laing Metro Limited, 2007, Schedule
1.5). To date, these counts have been designed to directly measure boardings, alightings, and
loads at each station once (per counting period) for each scheduled service. They indicate
31
utilization rates and capacity issues on Overground services, of interest to both TfL and
LOROL. However, because of the small sample size, these counts are likely not statistically
sound.
Passenger counts do not directly indicate demand at the individual origin-destination
(OD) flow level, nor do they describe how passengers use the Overground in conjunction
with other modes (e.g. the London Underground). Such information is primarily of interest
to TfL, and can be derived from OD flow matrices. Currently, the only OD matrix available
to Overground analysts and tactical planners comes from the RailPlan strategic model,
which in turns depends on the results of LTDS, London’s regional transport model, which
uses household surveys and census data as inputs . It is available only for the AM Peak, is
out of date and is based on very small sample surveys (Warner, 2010). As a result, it may
not accurately reproduce current demand patterns at the OD flow or station (i.e. boarding
or alighting) level.
Broadly speaking, Overground management (Bratton, 2009; Smales, 2009) have expressed
the need for a strategy that provides them with the same analytical quantities with which
they are used to working, but does so in a cheaper and more timely manner than is currently
available. The next section proposes a means to accomplish this, primarily through the
adoption and combination of automatic data sources.
3.2
A Synthetic Approach for the London Overground
In general, data from automatic systems are cheap and plentiful but do not capture complete
information from every passenger. Manual counts and surveys can fill some of the gaps left
by automatic systems, but are expensive to gather and therefore often insufficiently sampled.
Any source, taken alone, has some inherent ambiguity. This chapter, along with Chapters 4
and 5, seek to illuminate the limitations of each source and design the most effective strategy
to use them all together. This following section proposes such a strategy that uses automatic
data to meet the London Overground’s analytical requirements.
Several sources of automatically collected data on passenger quantities and behavior, each
with its own limitations, are readily available but as of yet largely unused in analysis and
management of the Overground. Electronic transactions from the Oyster smartcard ticketing
system describe individual journeys on the TfL rail network, but only a some fraction of all
journeys. Ticket gatelines, where present, automatically provide aggregate counts of station
entries and exits, but do not distinguish between passengers of different services at a given
station. With the delivery of new rolling stock, each Overground train will automatically
weigh and electronically report its passenger payload over the length of each trip. It is
hoped that these “loadweigh” systems on new rolling stock can provide a cheaper and more
statistically sound alternative to the manual on-board counts, but they require calibration
and will not indicate station boardings and alightings nor passenger origins and destinations.
None of these electronic data sources, taken alone, tells the complete story of how passengers use the Overground. Used in conjunction, what they may lack in completeness they
may make up for in quantity, variety, and cost. One objective of this thesis is to develop
ways to combine the various automatic data sources, and to target manual data collection
resources for maximum cost-effectiveness, to meet the needs of Overground managers.
32
The following data sources, are available for the development of the proposed approach.
• 100% samples of Oyster journey data for selected blocks of time. As a function of
London’s fare policy for rail journeys, transactions from its smartcard ticketing system
record the stations and times of entry and exit for each journey. As mentioned, this
data source does not cover journeys made using other fare payment methods.
• Aggregate gateline counts of entries and exits at stations with Overground services.
Gatelines automatically record the total entries and exits over each fifteen-minute time
interval, including passengers using non-Oyster fare media.
• Loadweigh measurements from new rolling stock, which will automatically sense and
report the weight of the payload of each rail car. These weight measurements can be
transformed into passenger counts through calibrated models relating passenger counts
and weights.
• A complete set of manual passenger counts conducted in the Spring of 2009, covering all weekday services on the entire Overground network.
• A network representation of the London Underground (LU), London Overground
(LO), Docklands Light Railway (DLR), and selected National Rail (NR) services. The
particular network model to be used is developed by London Underground as part of
their Rolling Origin and Destination Survey (RODS).
This thesis proposes to use the above automatic data sources to meet the immediate
needs of the Overground’s managers through the following.
• Estimate passenger loads on trains directly from loadweigh data systems. This requires
calibration of the loadweigh systems to understand the associated measurement error,
as discussed in Chapter 4.
• Use a mathematical process to estimate origin-destination flows by combining those
passenger loads with automatic gateline entry/exit counts, representative Oyster journey data, and selected strategic manual counts. This requires a significant modeling
effort, as discussed in Chapter 5.
• Using the models developed for OD estimation, assign the estimated OD matrix to the
Overground network to determine the total number of boardings at each station. This
is also discussed in Chapter 5.
• Estimate the total number of trips on the Overground (where a trip can include multiple
boardings) as the sum of the OD matrix. Note that the current strategy does not
provide estimates of this quantity.
Table 3-1 summarizes the current and proposed strategies.
33
Analytical
Quantity
Train Loads
OD Matrix
Boardings &
Alightings
Total
Ridership
Data
Source
Manual
Counts
LTDS/
Railplan
Manual
Counts
N/A
Current
Temporal
Statistical
Aggregation Basis
Train Trip 1 Day
Data
Source
Loadweigh
AM Peak
Only
1 Day
Train Trip
1 Day
Oyster &
Loadweigh
& Gatelines
OD Matrix
N/A
N/A
OD Matrix
Proposed
Termporal Statistical
Aggregation Basis
Train Trip Weeks/
Months
Time
Weeks/
Period
Months
Time
Period
Time
Period
Weeks/
Months
Weeks/
Months
Table 3-1: Current and proposed data collection strategies for the London Overground
3.3
Data Sources
The balance of this chapter describes the various data sources upon which the proposed
approach and other aspects of this thesis depend, including known issues for each source
that require investigation.
3.3.1
The Oyster Smartcard Ticketing System
As discussed in Chapter 2, the structure of London’s fare policy and technologies requires
most Oyster users to validate their cards upon all entries and exits to the system. The
centralized computer systems that support the Oyster system record and archive these entry
and exit transactions in an easily accessible modern database. As a result, disaggregate
Oyster journey data are cheap to gather in large volumes, and provide a prime source of
data on individual passenger journeys and aggregate OD flows.
Oyster transactions are stored in the Oyster “Central System” across a collection of
database tables – one for rail entries, one for rail exits, one for bus boardings, etc. A
specialized query has been designed to extract the necessary data from these tables to support
research purposes such as that described in this thesis. This query links data from these
tables with each other and with reference tables to produce a single table describing all
journeys recorded in the Oyster system (Gaitskell, 2008). Some fields of this table are
populated differently for bus and for rail journeys. For rail journeys, the information provided
includes:
• The Oyster card identifier (“card ID”), uniquely identifying each Oyster card in the
database, anonymized to protect passenger privacy. It is typically assumed in analyzing
Oyster data that each card ID represents a unique passenger.
• The station and time of first entry into the system.
• The station and time of last exit from the system.
• The date of the journey (as determined by the date of the entry transaction).
34
• The fare type of the journey (i.e. single fare, unlimited use, or a mix between the two).
• The fare paid.
• The innermost and outermost fare zones for which the journey was charged.
These data provide an extremely rich corpus with which to study many aspects of passenger demand, behavior, and experience on London’s public transport network. However,
Oyster data do not provide a complete picture for a number of reasons.
• Not everyone uses Oyster. The penetration rate across all TfL services is estimated to
be approximately 80% (Transport for London, 2009e), but varies in space and in time
across the TfL network (Chan, 2007).
• Some stations, including many of those served by the Overground, are ungated. Passengers using these stations in unlimited-use fare categories (e.g. weekly and monthly
travelcard users) are not required to validate their Oyster cards at ungated stations.
• Oyster data describe only the first and last station used on a given trip. TfL’s rail
network is integrated and complex, with many journeys involving free interchanges,
many stations served by numerous services, and multiple possible routings between
station pairs. Many Oyster records are inherently ambiguous with regard to whether
the Overground was in fact used at all, depending on the available routes between the
origin and destination stations.
• The timestamps of all Oyster transactions are stored in the Central System in a truncated form – they indicate the time of day in minutes but not in seconds. Consequently,
the times of passenger entry and exit available for research purposes are less precise
than would be desired.
Nevertheless, as discussed in Chapter 5, Oyster data will play an important role in
estimation of OD matrices for the Overground. The methods for estimating OD matrices
that will be considered generally depend on some prior estimate of the OD matrix (also called
a “seed matrix”) to produce good results. The Oyster system will provide that estimate.
Oyster data will also be used to analyze passenger station arrival behavior in Chapter 6 and
passenger journey times in Chapters 8 and 9.
3.3.2
“Loadweigh” Train Payload Weighing Systems
The term “loadweigh” refers to electronic systems that estimate train payloads from measurements of air pressure in suspension systems (Interfleet Technology, 2004). All new Overground rolling stock are equipped with loadweigh systems for the explicit purpose of estimating passenger loads. Loadweigh data, although not yet tested on the Overground, are
expected to allow estimation of actual loads on trains with reasonable accuracy, however
saying nothing about boardings and alightings at each station. Experience with these systems at other Train Operating Companies is positive (Southern Railway LTD, 2009), but
they have not tried to use these data in conjunction with other sources such as Oyster.
35
Loadweigh systems measure the weight of a train’s contents, and thus report their measurements in units of mass (which of course is directly proportional to weight) (Interfleet
Technology, 2004). As a result of variability in passenger weights and possible measurement
error in the loadweigh system itself, there is expected to be some error associated with the
estimates of passenger loads derived from loadweigh data. Chapter 4 will explore this issue
further.
3.3.3
Station Gatelines
Entry and exit counts from station gatelines are typically used by the London Underground
to scale up the results of manual origin-destination surveys (Maunder, 2003) or Oyster-based
seed matrices (Wilson et al., 2008). In the Overground case, a large portion of traffic starts
or ends at stations shared by multiple rail providers, so gateline data are ambiguous with
respect to whether a given passenger used the Overground at all. Eleven stations (out of 56)
are both fully gated and exclusive to the Overground. For the AM Peak period in the Spring
of 2009, these eleven stations admitted an estimated 8,600 passengers out of the estimated
39,000 total Overground boardings (22%). Another 21 stations are gated but provide access
to other London Underground or National Rail services.
3.3.4
Manual Passenger Counts
Under the current manual counting scheme, the boarding, alighting, and on-train load are
sampled at most once for each scheduled service at each station. This presents the obvious
statistical issue of assuming there is no day-to-day variation in demand which, lacking any
other data, is remedied only at unreasonable cost. Nevertheless, these manual counts should
be of use in testing and validating OD estimation methodologies, especially in the absence
of complete loadweigh data.
Overground management expects to continue manual counts on non loadweigh-enabled
portions of the network until new rolling stock is delivered. However, the concession contract
allows LOROL to substitute loadweigh estimates for manual counts as loadweigh becomes
available. This, combined with recent cost reduction initiatives at TfL, severely limits the
ability of TfL to sponsor additional manual counts in the future (Smales, 2010).
3.3.5
Network Representations
TfL maintains (at least) two detailed representations of London’s public transportation network. Corporate and strategic planning groups developed and use the RailPlan model, which
represents all bus and rail modes in London, for long-term investment planning. RailPlan
is implemented inside the proprietary EMME/2 transportation planning software package,
and is regularly updated and modified by staff across TfL for various planning tasks.
The Strategy and Service Development group at London Underground has developed a
rail-only model, focused on its own network but including competitive services, for use in
its Rolling Origin and Destination Survey (RODS is in fact a combined OD estimation and
network assignment model). It is implemented as a suite of custom in-house software tools
36
and represents the transport network as a set of easy-to-share flat files. The RODS model
and data are well explained in internal TfL documentation (Maunder, 2003).
The network representation from the RODS model will be used in this work because
of its open and easy-to-share nature, and because it was designed and implemented with
OD estimation in mind. It was not, at the outset, sufficiently detailed with respect to the
Overground, but the additional detail was straightforward to add. Most of the necessary
updates were to
• distinguish Overground services from other National Rail services at certain stations,
• reflect current Overground service patterns and frequencies,
• and explicitly represent entries, ticket halls, and exits at Overground stations lacking
those features in the model.
3.3.6
Additional Data Sources
Train Control Systems – Modern train signaling, supervision, and control systems record
extensive data indicating actual railway operations. Many systems, including the National Rail network used by the Overground, record the movements of every train on
the network. The use of this type of data to support operating strategies and tactical
planning has been researched extensively, for example by Rahbee (1999, 2006), Vescovacci (2001), Lee (2002), and Carrel (2009). This thesis does not deal with this type
of data directly, but uses performance data and cites other analyses of Overground
operations both derived from these type of data.
National Rail Performance Monitoring Systems The National Rail network has an
elaborate performance monitoring and delay attribution framework in place. Its TRUST
system uses data from signal and control systems to monitor and record all train movements (Office of Rail Regulation, 2010). These records are used to calculate the Public
Performance Measure (PPM), a measure of train on-time performance at terminals
(Office of Rail Regulation, 2008). A complex delay attribution methodology, requiring
substantial manual inputs, is used to allocate delays to responsible parties (TOCs,
Network Rail, etc) for the sake of performance monitoring and financial remuneration
(Network Rail, 2009). Chapters 8 and 9 use some of these outputs to evaluate the proposed measures of service quality and the outcome of the tactical planning intervention
on the North London Line.
The London Travel Demand Survey The London Travel Demand Survey (LTDS) is a
London-wide household travel survey updated on a rolling basis over time. This survey, along with census data and other sources, underpins an area-wide transportation
planning model (also called LTDS). One output of that model is an estimate of public transport travel in London on a zone-to-zone basis (zones in this case are traffic
analysis zones, rather than fare zones).
Railplan Regional Public Transport Model The LTDS estimates of public transport
travel become inputs into the RailPlan regional public transport assignment model.
37
Railplan uses a detailed representation of London’s public transport network to estimate demand for existing services, and to model the effects of proposed changes to
the network and of forecast economic growth (cf AECOM, 2006). It is used almost
exclusively to model transport for the AM Peak period. Railplan does not use direct
measurements of the sort discussed above to estimate current conditions. Instead, it
is, from time to time, validated against other estimates of demand. As has been found
(AECOM, 2006) and will be shown in Chapter 5, Railplan’s estimates often diverge
from other more believable estimates by 50% (or more) at fairly aggregate levels. Nevertheless, Railplan is currently the only source of origin-destination matrices used by
the Overground for various analysis and tactical planning tasks.
Public Timetables TfL has access to public timetables for Overground services in plaintext formats. These timetables become an integral part of the work in Chapter 6, 8,
and 9.
38
Chapter 4
Calibration of Loadweigh Systems
The term “loadweigh” refers to electronic systems that estimate train payloads from measurements of air pressure in suspension systems. Loadweigh systems measure and record
the weight of a train’s contents in units of mass. Passenger loads are inferred from these
measurements of weight by means of an estimated or assumed average passenger weight
(Interfleet Technology, 2004). As a result of variability in passenger weights and possible
measurement error in the loadweigh system itself, there will be some error associated with
the estimates of passenger loads inferred from loadweigh data.
This chapter develops a methodology by which to infer train loads in units of passengers
from loadweigh measurements in units of weight. The basic idea of this methodology is
to regress loadweigh data on corresponding manual passenger counts to estimate average
passenger weight and vehicle tare (i.e. unladen) weight. These two parameters can then be
applied to infer passenger load from new loadweigh data in the future. The methodology
also provides an estimated bound on the magnitude of random error associated with these
estimates.
Section 4.1 reviews the little academic and industry literature available on the topic.
Section 4.2 discusses the various sources of error in loadweigh systems and develops a simple
linear regression model for calibrating loadweigh systems. Section 4.3 presents an exploratory
analysis of a sample of loadweigh data and manual counts from the London Overground.
Section 4.4 applies the model to data from the London Overground and presents the results.
Section 4.6 draws conclusions and offers some recommendations.
4.1
Literature Review and Industry Experience
Loadweigh systems were developed in the UK by British Rail Research and have since been
commercialized by aftermarket vendors and by rail car manufacturers such as Bombardier
(Interfleet Technology, 2004). While they have been used in the UK for over a decade (Smale,
2010), in some cases with documented positive results (e.g. Southern Railway LTD, 2009),
very little analytical literature exists on the subject. Most of the accumulated knowledge
and experience with these systems appears to be within industry parties, such as equipment
suppliers, information service providers, and the railways themselves.
In a telephone interview, Smale (2010), director of UK railway information services
39
provider Demon Information Systems, reports from internal company research that loadweigh data are “accurate to within ±20 passengers at a 95% confidence interval for a threecar train.” He reports that this error is not related to the passenger load, and so is larger as
a percentage of the load at smaller loads. He reports that average passenger weights of 75-85
kilograms have been estimated in previous calibration exercises, and recommends using 80kg
for the London Overground. These exercises have used very careful and expensive manual
counts taken by two surveyors on each rail car. Technical details as to how the calibration
was accomplished from loadweigh data and passenger counts are not available. Finally, he
reports that the loadweigh measurements recorded and provided by Bombardier, the manufacturer of the new Overground fleet, are in fact the average of a series of measurements
taken at twenty cycles per second as trains travel between consecutive stations.
Bombardier Transportation (2004) conducted a systematic but small-scale study involving three different kinds of tests, each conducted on a single train trip with encouraging
results. In the first test, they loaded a known amount of weight (17,970kg to be precise)
onto a train which was then run along the length of the route. They observed some variation
in the en route loadweigh measurements, likely as a result of the dynamics of the train’s suspension, but all recorded measurements (i.e. the averages of the 20hz measurements) were
within 5% of the (constant) true weight. In the second test, they ran a train in passenger
service and “a number of observers” counted the number of occupants at each station. They
multiplied these passenger counts, which were never more than 250, by an assumed average
passenger weight of 80kg and compared the estimated weight to the measured weight. The
estimated was at times larger than the measured weight and at times smaller, but they never
diverged by more than 6.25%. In the final test, 34 passengers of known weight rode a test
train along its run, circulating en route between cars on the train. The measured weight
diverged from the known weight by more than 5% in only one instance (out of 12) when
there was a temporary equipment failure.
This study concerned Bombardier class 375 rolling stock, which are very similar in design
to the Overground’s new class 378 fleet, and concluded that their loadweigh systems were
fit for purpose. It acknowledged that assuming an average passenger weight of 80kg can
introduce some error, especially for particular days, but that “fluctuations of this nature will
even themselves out over a period of time and multiple journeys over the same route.”
Researchers in Copenhagen, Denmark have analyzed data from built-in loadweigh systems and from expensive aftermarket infrared passenger-counting systems for their S-Train
suburban rail network. Unfortunately, the S-Train operator has not yet allowed the authors
to publish their work in detail, so personal communications, presentation slides (Nielsen
et al., 2008a), and an abstract (Nielsen et al., 2008b) are the only available references for
this work. The researchers compared measurements from both systems with corresponding
highly accurate manual counts taken from recorded video footage (Nielsen, 2009b). They
used regressions to make these comparisons (Nielsen, 2009a) but the precise form of the
regressions has not been revealed. Their presentation slides indicate that the estimates of
passenger loads derived from loadweigh data were unbiased and had a random error with a
standard deviation of about 14 that did not vary meaningfully with the actual load. The
infrared systems had a smaller standard deviation of 0.75 but for loads above 50 passengers
had a negative bias of about 7%.
(Nielsen et al., 2008b) concluded that, for their particular client, loadweigh systems were
40
preferable to infrared counters despite the much larger random error because loadweigh
systems were unbiased and available on all trains at no extra cost. After analyzing the
loadweigh systems, they went on to estimate OD matrices from an existing survey-based
OD matrix and passenger loads inferred from loadweigh data (similar to what is proposed
here). This is discussed further in Chapter 5. They have implemented a production system
for the S-Train operator that automatically estimates passenger loads and OD matrices on a
daily basis for use in management, planning, and even revenue allocation among competing
services. To date, this system assumes a single average passenger weight across the entire
S-Train network for all times of day and and days of the year. The researchers plan to further
explore the variation in passenger weights across these dimensions.
4.2
Model Development
Any estimate of passenger loads from loadweigh measurements will at some level be based
on assumptions or inferences about passenger weights. The model proposed here is consistent with the literature discussed in the previous section in that passenger weights are
parameterized in terms of a single average value. This value can potentially change over
time or across market segments, but any group of passengers is described only in terms
of their average weight. This average weight, as well as other calibration parameters, will
be estimated through pairwise comparison of loadweigh measurements with corresponding
manual passenger counts. These estimates of passenger loads will thus be affected by the
following four sources of error.
• Random measurement error in the loadweigh system – random error can occur in the
loadweigh system through any number of known or unknown factors, including the
dynamics of train motion and suspension systems.
• Systematic measurement error in the loadweigh system – a constant error associated
with the loadweigh system, for example by a non-zero tare weight.
• Variation in true average passenger weight – the difference between the actual average
weight of passengers and the assumed or estimated value.
• Random measurement error in the manual passenger counts – random error associated
with the manual counts with which loadweigh data are compared.
For a single loadweigh measurement and corresponding manual count taken on a certain
train at a certain time, let
W = the loadweigh measurement,
η = the random error associated with the loadweigh measurement system itself,
α = the systematic measurement error of the loadweigh system,
C = the true number of passengers on that train at that time,
ω = the random error associated with the manual count,
41
β = the true average weight of all passengers (on all trains),
ν = the random error associated with the actual average weight of passengers on the train
in question as compared to β.
The relationship between loadweigh measurements, manual counts, and these various
sources of error can be characterized by the equation
W − α + η = β(C + ω) + ν.
(4-1)
Assume that η, ν, and ω are symmetrically and independently distributed each with mean
zero. Let
ε = βω + ν − η.
Then ε also has a mean of zero. Equation (4-1) can be rewritten as
W = βC + α + ε.
(4-2)
This equation satisfies the form of a single-variable linear regression, and so its parameters
(β, α, ε) can be estimated by the method of ordinary least squares (OLS) (Greene, 2007).
Let the OLS estimate for a parameter λ be denoted λ̂. Substituting the estimated
parameters into Equation (4-2) and solving for C yields
C=
W
β̂
−
α̂
β̂
−
ε̂
β̂
.
(4-3)
This equation is important for two reasons. Firstly, it makes apparent the interpretation of
the two following terms. α̂β̂ is the estimate of the tare weight (i.e. the systematic error) of
the loadweigh system in number of passengers. Likewise, β̂ε̂ is the estimate of total random
error for a particular observation in number of passengers.
Secondly, it can be used to estimate passenger loads from new loadweigh measurements
(i.e. those lacking corresponding manual counts). Consistent with application of linear regression models, such an estimation assumes that ε for these measurements is equal to zero,
which yields
W −α
.
(4-4)
C=
β̂
In other words, to estimate the number of passengers, subtract the tare from the loadweigh
measurement and divide the result by the average weight per passenger.
The standard deviation of β̂ε̂ is also an important quantity. It can be interpreted as an
estimate of the random error in passenger loads inferred from loadweigh data. This random
error consists of the random loadweigh measurement error and the variability in average
passenger weight; factors which are beyond control for a given loadweigh system. In fact
this estimate is an upper bound of the standard deviation of random error introduced by
these factors. It is an upper bound because additional error is introduced in the calibration
process by the manual counts (i.e. ε depends on ω). The bound is tight if and only if
the manual counts with which it was calibrated were perfect (i.e. ω = 0). This bound is
42
important because it indicates the overall statistical reliability of passenger load estimates
derived from loadweigh data. It will be referred to here as the “error bound” for loadweigh
data, and will be signified by the variable δ.
Assume that the random error in passenger loads inferred from loadweigh data is normally
distributed with mean zero and standard deviation equal to the error bound δ = sd β̂ε̂ .
Then, by the properties of the normal distribution, passenger loads inferred from loadweigh
data should be accurate to within at most ±1.95δ at the 95% confidence interval.
4.3
Exploratory Analysis
The London Overground provided a sample of 13,121 weekday loadweigh measurements from
13 different units (i.e. full 3-car trains) serving the North and West London Lines from 23
November through 6 December, 2009, inclusive. These data were extracted from on-board
systems and processed into usable formats by Bombardier Transportation, the rolling stock
provider. Each observation reports a number of elements, including train unit number,
departing station, date and time of departure, and loadweigh measurement in kg. It should
be noted that about half of the units on the North and West London Lines were from the
new loadweigh-enabled fleet at the time of this data sample.
Corresponding manual counts were also provided for 1,253 of these observations over 80
different vehicle trips on 24 November and 1-2 December, 2009. This is the data set on
which the model from the previous section will be estimated. 115 of these observations were
taken on the West London Line, the balance on the North London Line. The manual counts
were taken by a pair of observers at each platform, and are anecdotally reported by their
provider to have an accuracy of ±20 passengers at a 95% confidence interval. It should be
noted that the provider of these counts explicitly recommends the use of a more intensive
counting scheme, with two observers on each car, for the purposes of loadweigh calibration
(Smale, 2010)
Figure 4-1 plots the distribution of these loadweigh measurements, which range from 0kg
to 47,060kg (588.25 passengers at 80kg each). This plot illustrates that loadweigh data, at
least from the Overground fleet, vary smoothly over a considerable range.
Figure 4-2 plots loadweigh measurements against time of day for a random 10% sample
of the provided data. It illustrates that the highest loadweigh measurements indeed occur
in the morning and evening peaks experienced throughout the TfL network.
Figure 4-3 plots loadweigh measurements against time of day for all observations on a
single link in the Overground network. The selected link is from Canonbury to Highbury &
Islington, generally held to be the peak load point of the North London Line during the AM
Peak period. This plot shows directional effects, where loadweigh measurements are greater
in the morning than in the evening, consistent with expectations.
It also illustrates some day-to-day variation, with variance in measurements taken at the
same time of each day (e.g. just after 20:00). Being taken at the same time of day at the same
location, these measurements are likely taken from the same scheduled service. As further
discussed in Section 4.5 this indicates the presence of day-to-day variability in on-train loads
that the Overground’s current single-sample on-board counts do not capture.
43
1.0
0.8
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Figure 4-1: Cumulative distribution of London Overground loadweigh measurements
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Time of Day
Figure 4-2: Loadweigh weight vs. time of day (random 10% sample)
Figure 4-4 plots loadweigh measurements against corresponding manual counts for all
stations and for Stratford and Richmond, the two main North London Line terminals. It
shows a clear but not perfect linear correlation between the two variables, with a correlation
coefficient of 0.927 for the whole data set. This correlation is significantly higher for the
observations from the terminals, with a coefficient of 0.992.
The higher correlation at terminals could be explained by more accurate passenger counts
at those locations, which could result for the following reasons. Overground trains generally
spend much longer at terminals waiting to depart than they do at stations en route, so
observers have time to count accurately the number of boarding passengers. Moreover,
at terminals there is little if any simultaneity in passenger boarding and alighting, which
simplifies the passenger counting task. In the lexicon of the previous section, ω should be
smaller for manual counts taken at terminals. The general shape of these plots suggest that a
44
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Figure 4-3: Loadweigh weight vs. time of day for peak load point of London Overground
network (Canonbury to Highbury & Islington)
linear regression model is an appropriate modeling framework. They also suggest that such a
model will have a better fit and produce more accurate parameter estimates for observations
taken at terminals than for observations taken en route.
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Figure 4-4: Loadweigh weight vs. manual count data
4.4
Calibration Results for the London Overground
The model of Equation (4-2) was regressed on the calibration data set in the following ways.
Pooled – the model was estimated on the entire calibration set of 1,253 paired loadweigh
and manual count observations.
45
Unit Segmentation – the model was estimated on data for each of the 13 full-train units
separately. This series of regressions explores the possibility of variability in the functioning of loadweigh systems across different trains. It can be considered an unrestricted version of the pooled model. The observations are not uniformly distributed
across the different units. The number of observations per unit ranges from 15 to 267.
The two summary statistics as well as the observation-weighted estimate of β were also
estimated for the joint results of this entire series of regressions.
Terminals Only – the model was estimated on data from just the two main North London
Line terminals. This reduced data set contains only 49 observations, 25 from Stratford
and 24 from Richmond. This regression should indicate whether the manual counts
from terminals are more accurate than manual counts taken en-route. The regression
was also run on terminals-only data for the two units with at least 10 observations at
terminals.
The regressions were estimated using the open source statistical programming language
and environment R (The R Project,
2009). In addition to parameter estimates, the adjusted
2
R and the error bound, δ = sd β̂ε̂ , were calculated for each regression.
For all of these regressions, β is expected to be in the 75 - 85 kg range. There is no
particular expectation on the sign or magnitude of α, nor is there an expectation as to how
different the parameters from the unit segmented regressions should be from each other.
Estimates of α that are small in magnitude or are not statistically significant will indicate
small or non-existent systematic bias in the loadweigh measurement systems. Based on the
literature, it is expected that the variance of the residuals of these regressions will be constant
(i.e. homoscedastic). The statement of Smale (2010) that loadweigh data are “accurate to
within ±20 passengers at a 95% confidence interval for a three-car train” would be supported
by finding a δ of approximately 10.
Table 4-1 shows the results of these model estimations. All estimates of β, the average
weight per passenger, are statistically significant at the 0.1% significance level. β for the
pooled and terminals only model, 77.3 and 81.4, respectively, are both within the expected
range but substantially different from each other. The estimates of β for the unit segmented
regressions cover a wide range, from 62.4 to 85.0. In a standard F-test, the disaggregation
of the pooled model into the joint unit segmented model is overall statistically significant at
the 0.1% level.
The estimate of α, the tare weight, is statistically significant in some of the models
estimated on all of the calibration data. The sign is positive in some cases, and negative
in others. The magnitude ranges widely for the unit-segmented regressions, from 115kg
(estimated 1.5 passengers) to 3,686kg (estimated 47.8 passengers).
The terminals-only regressions appear to provide substantially better results than those
estimated on data from all stations. The estimates of β for the two units with at least 10
observations, 79.9 and 79.7, are close to the estimate over all terminal observations and are
almost identical to each other. The estimate of α is, perhaps tellingly, small in magnitude (at
most 6 passengers) and in all cases not statistically significant. In terms of the adjusted R2
and the estimate of the error bound, δ, the terminals-only regression results are far superior:
its R2 is 0.98 compared with 0.86 for the pooled regression and 0.88 for the joint results of
46
the unit segmented regression.
Perhaps most importantly, the terminals-only regression estimates a δ of 10.8, and 5.0
and 11.4 for the two segmented units, very much in line with industry expectations. The
pooled and joint unit segmented regressions, both estimated using observations from all
stations, estimate a δ of 35.3 and 31.9, respectively.
Model
Obs.
Trips
Avg
Tare
Tare in
Error
Weight
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Bound
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α
Pass.
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δ
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7.4
35.3
0.86
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80 77.3
Unit Segmentation
378007
139
8 62.4
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15
3 66.1
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223
16 78.4
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191
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56
3 77.1
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8 80.4
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1,235
80 78.2
Terminals Only
49
49 81.4
Unit Segmentation (Terminals Only)
378010
10
10 79.9
378017
10
10 79.7
***
572 ***
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2,161
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115
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1,442
453
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29.1
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36.3
30.9
25.3
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31.9
10.9
***
***
-174
475
-2.2
6.0
5.0 1.00
11.4 0.99
**
***
***
Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table 4-1: Loadweigh calibration results
Figure 4-5 plots the residuals, ε̂, against the manually counted number of passengers
for two of the estimated models. It shows the residuals from the regression on all data
with the lowest δ, the joint unit segmented model, and on the pooled terminals-only data.
For the regression on all data the variance of the residuals appears approximately constant
at passenger counts above 100 or 150 passengers. The standard deviation (in kg) of the all
residuals and for residuals only from observations at terminals are 2,502 and 951, respectively.
In the terminals only regression the variance of the residuals appears constant throughout,
and is clearly much less than the variance of the residuals from regressions estimated on all
of the data. In this regression, the standard deviation of the residuals is 885.
These results indicate the desirable property of homoscedasticity in the error terms of
the regression models. More importantly, they indicate that the fit between manual counts
and loadweigh data is much tighter for observations at terminals that at other stations, even
when the model is estimated with the entire data set. The implications of this difference is
discussed further in the following section.
47
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Figure 4-5: Residual vs. manual count for all data (unit segmented) and terminals-only
(pooled)
4.5
Variability of On-board Loads
The key analytical quantity that the London Overground looks to loadweigh data to provide
is on-board loads for each scheduled service between each pair of stations. Given the results
of the previous section, it is possible to start to assess the statistical quality of the existing
on-board counts, sampled precisely once per counting period, that loadweigh systems are
intended to replace.
Figure 4-6 shows loadweigh measurements for trains traveling from Canonbury to Highbury & Islington between 08:00 and 09:00 – the peak load point of the North London Line
in the peak hour. At the time these counts were taken, the 08:09 train from Stratford to
Richmond was the only service in the timetable on this link between 08:20 and 08:30. It
is thus reasonable to assume that those loadweigh observations on this link between those
times were taken on that scheduled service. It is necessary to make this assumption because
loadweigh data are not yet associated with specific scheduled services.
There are 7 observations (from 7 different days) in Figure 4-6 between 08:20 and 08:30,
with measured loads from 37,870kg to 42,400kg. Using a β of 80kg, the load in number of
passengers estimated from these measurements range from 473 to 530, with a mean of 506.
The single manual calibration count associated with this link for this scheduled service was
475 passengers. For the trip on which this scheduled service was manually surveyed, this
link was indeed the peak load point, as is generally assumed for westbound travel on the
North London Line in the AM Peak period. If the mean of these estimated passenger loads
(i.e. 506) is taken to be the true average, the single-sample manual estimate of the average
peak load on this service (i.e. 475) was short by 31 passengers, or 6.1%.
The standard error of the 7 load estimates is 18.5 passengers. This can be interpreted,
somewhat speculatively, as an estimate of the standard deviation of passenger load estimates
48
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Figure 4-6: Loadweigh weight vs. time of day for peak load point data
on this link on this service including the random error introduced by the loadweigh system
and calibration process. Consequently, an estimate of the “true” average load from a single loadweigh sample would be accurate to within ±37 passengers at the 95% confidence
level. However, with 14 loadweigh samples the accuracy could be improved to within ±10
passengers at a 95% confidence level (i.e. a standard deviation of 5).
In the previous section, the best estimate of the error bound associated with passenger
loads inferred from loadweigh data was 10.8. Under the assumption of independent and
normally distributed errors this implies that the standard deviation of “true” passenger load
with respect to the “true” average load is 7.7 passengers (i.e. 18.5−10.8). The error bound of
10.8 was estimated using data only from terminals. The lowest estimate of the error bound
using data from all stations was 31.9. This can be interpreted, again somewhat speculatively,
to imply a standard deviation of just over 21.1 passengers for the error associated with manual
counts at non-terminal locations. The total standard deviation of one manual count, with
respect to the “true” average on this link for this scheduled service, can then be estimated at
28.8 (i.e. 21.1 + 7.7), implying an accuracy of ±57.6 at the 95% confidence level. For reasons
of cost, the Overground is unable to take more than a single manual count of each scheduled
service per counting period.
The analysis in this section indicates that a single estimate of passenger loads from
loadweigh data may, at non-terminal locations, be more accurate than a single manual
passenger count. Moreover, the automatic and easily obtainable nature of loadweigh data
may be exploited to obtain substantially more accurate results at effectively zero marginal
cost.
The precise numerical results of this section are somewhat speculative. They should not
be assumed to be generally representative of the variability of passenger loads or the error in
passenger counts on the Overground network as a whole. A much larger sample of loadweigh
data (i.e. for many more links and scheduled services) should be used to understand the
statistical nature of these factors.
49
4.6
Conclusions and Recommendations
This chapter analyzed loadweigh data from the London Overground, and used corresponding
manual passenger counts to calibrate a model for estimating passenger counts based on
loadweigh data. This section presents first some conclusions drawn from the analysis in this
chapter, and next some recommendations based on those conclusions.
Conclusions
The foremost conclusion drawn from these results is that there is no basis for rejecting the
practices for using loadweigh data recommended by Smale (2010). Rather, analysis of a
limited data set (from terminals only) suggests that the recommended assumptions of an
average passenger weight of 80kg and a 95% confidence interval of ±20 passengers, with no
tare weight, (Smale, 2010) is in fact reasonable.
A corollary to this conclusion is that the manual counts used here are generally of insufficient quality for calibrating loadweigh systems. This is acknowledged by the provider of the
counts. The primary explanation is that the counts used here were taken by a single pair
of observers on each station platform, whereas the preferred counting strategy for loadweigh
calibration is to employ a pair of observers on each car (Smale, 2010).
That said, the regression results support the theory that counts taken at departing terminals are more accurate than counts at stations served en route. The likely explanations
for this are that the surveyors have much more time to count passengers and passengers typically alight and board more sequentially at terminals than at stations en route. The number
of paired observations of loadweigh measurements and manual counts taken at terminals is
limited to only 49 out of the whole set of 1,253. The regression on this limited set produces
results very close to prior findings, specifically:
• It estimates the average weight of passengers at 81.4kg, with high statistical significance. This is only 1.8% different from the recommended value of 80kg.
• It estimates an error bound of 10.8kg. This is the upper bound of the standard deviation of random error in passenger loads inferred from loadweigh data. Assuming
normally distributed random error, this amounts to a 95% confidence interval of ±21.2
passengers, as compared to the recommended ±20 passengers.
• It estimates a relatively small tare weight of 328.6kg (4.0 passengers), but this estimate
is not statistically significant. For individual units, the estimate of tare weight is of
the same order of magnitude and also not statistically significant. That is, there is no
evidence to suggest that the tare weight is other than zero.
In terms of methodology, the linear regression model used in this chapter appears suitable
for comparing loadweigh data with manual passenger counts. Because the residuals in these
regressions are of approximately constant variance, the method of ordinary least squares is
adequate to estimate this model.
A preliminary analysis of the temporal variability of passenger loads on scheduled services
found that fewer than 20 loadweigh samples, available at effectively no marginal cost, would
50
be sufficient to estimate the “true” average passenger load to within ±10 passengers at the
95% confidence level.
Recommendations
Given the results and conclusions of this chapter, it is recommended that loadweigh data be
pursued as a low-cost and (sufficiently) reliable source of data on passenger loads on trains.
This applies to the railway industry in general and specifically to the London Overground.
Naturally, multiple loadweigh samples should be used to estimate the average load on any
particular scheduled service for any particular link in the network. The number of samples
required depends on the desired accuracy.
Additional research should be conducted into the nature and magnitude of the various
sources of error associated with passenger loads inferred from loadweigh data. The weakness
of the analysis in this chapter stems primarily from the low quality of the manual counts
against which loadweigh data were compared. To remedy this and other issues, the following
are recommended.
• More and better calibration data should be gathered and paired with corresponding
loadweigh data. The regressions from this chapter should be used to re-estimate the
calibration parameters and to estimate the error bound.
• If it is believed that there is no bias in the calibration parameters at terminals, these
data could be gathered at terminals under the same counting procedures used to
gather the data analyzed here. If data is required at stations other than terminals,
“calibration-quality” counts should be taken, with procedures to ensure greater accuracy than was found in the overall data used here.
• In addition, the calibration-quality counts or additional terminal counts should be used
to explore variability in the parameter estimates and error bound across different rolling
stock units. If such analysis indicates significant differences between individual rolling
stock units, individual calibration of all future rolling stock units as they are delivered
may be recommended. Additionally, it should be investigated whether the actual
loadweigh equipment on each unit has calibration parameters that can be adjusted.
• As identified by Nielsen et al. (2008a), additional analysis should be conducted at
different times of year to assess the systematic variation in average passenger weights
correlated with seasons and weather. It is possible that such variation could be ignored,
but this question should be explored.
• Controlled experiments, such as the first and third tests described by Bombardier
Transportation (2004), should be conducted on Overground rolling stock. This would
entail placing a known amount of weight (be it in sandbags or human participants) onto
loadweigh-enabled trains, running them along the length of the line, and comparing the
loadweigh measurements to the known value. The primary purpose of such experiments
is to understand the pure measurement error associated with loadweigh systems.
51
Applied to the Overground, these recommendations should of course be tempered by cost
considerations. For example, the Overground may not be able to afford multiple series
of calibration-quality passenger counts in the future. In this case, they may assume that
the parameter and error bound estimates derived from a first series of counts, or even the
estimates from this chapter, apply to all rolling stock at all times.
52
Chapter 5
Origin-Destination Matrix Estimation
Passenger demand for a public transport network can be expressed as a matrix of passenger
origin-destination (OD) flows (an OD matrix ). OD matrices are one of the most important
inputs into many public transport planning and management applications (Meyer and Miller,
2001). This Chapter is primarily concerned with the estimation of OD matrices for the
London Overground network. It develops, applies, and validates a methodology to estimate
OD matrices from multiple data sources, including (i) journey transactions from automatic
fare collection (AFC) systems (such as Oyster), (ii) manually counted and/or automatically
measured on-board passenger flows in the network, and (iii) station entry and exit counts
from automatic station gatelines. The balance of this section introduces some of the basic
concepts necessary to discuss this topic, and then describes the organization of this chapter.
In transport modeling, assignment refers to the process of estimating how passengers use
a given network to travel between their respective origins and destinations. One outcome
of the assignment process applied to an OD matrix is an estimate of the total utilization
of each link in the transport network. Such estimation depends crucially on models of
passenger behavior (e.g. path choice) and of the relationship between link flow and link
performance (i.e. congestion effects) (Meyer and Miller, 2001). These models, along with the
choices of how to represent the transportation network both spatially and temporally, will
be collectively referred to here as “assignment models.”
Estimation of an OD matrix given links flows (“OD estimation”), which is the primary
concern of this chapter, can be understood as the inverse of the assignment problem (Bierlaire, 2002). As such, it too depends on the assignment model. This should be intuitively
clear in that, to estimate an OD matrix from given link flows, it is necessary to know the
links used by passengers traveling between each origin-destination pair.
In addition, OD estimation often takes as additional input some prior estimate of the
OD matrix (also referred to as a “seed” matrix), which is important because there are often
infinitely many ways to construct an OD matrix to match the given link flows (Bierlaire,
2002). Historically, these prior OD estimates were expected either to be OD matrices directly
estimated from expensive manual surveys and requiring updating to account for changing
travel patterns, or to be OD matrices that came from regional transportation models that
were not calibrated on measured link flows (Cascetta, 1984).
To estimate time period level OD matrices for the Overground, a credible assignment
model must be adapted or developed. That assignment model will be used as part of an
53
OD estimation process which takes as input manually and automatically measured link flows
and an Oyster-based seed matrix. As discussed in Chapter 3, Oyster represents only a lower
bound on the true OD matrix (thus referred to here as a “fractional seed matrix”). In that
sense, the problem faced by the Overground is somewhat different from that addressed by
most of the established methodologies.
Sections 5.1 and 5.2 review some well-known assignment models and OD estimation
methods, respectively, with an eye towards practical application to the Overground. Section
5.3 draws on that review to propose a detailed strategy for estimating OD matrices from
AFC-based seed matrices and a flexible set of measured link flows. This strategy includes
an assignment model that is tailored to the context of the Overground. Section 5.4 presents
an exploratory analysis of data relevant to the proposed strategy. Section 5.5 presents and
validates the results produced by the proposed method, and compares the validation of the
estimated OD matrix to a validation of the existing Overground OD matrix produced by the
RailPlan regional model. Section 5.6 draws some conclusions and makes recommendations
for implementation.
5.1
Public Transport Network Assignment Literature
Review
Broadly speaking, assignment models are those models which are used to estimate the utilization of different parts of a transport network given an estimate of demand in the form
of an OD matrix. Passengers can be assigned to certain paths through the network, specific services in the network, or individual links on the network. Nuzzolo (2003) provides
a good review of public transport assignment models. What are referred to in this chapter as “assignment models” actually consist of a hierarchical family of models, only one of
which is, in the literature, referred to by this name. At the lowest level of the hierarchy are
supply models – those that represent the public transport network itself. The next level is
path choice models – behavioral models that describe how passengers identify, evaluate, and
choose among different paths through the network. The highest level is what are narrowly
referred to in the literature as “assignment models” – those which build on the other types of
models to estimate and report the utilization of the network in spatial, and possibly temporal, dimensions. Certain kinds of assignment models are associated with certain supply and
path choice models, so this distinction is somewhat arbitrary. This section reviews selected
literature on these members of the broad family of assignment models, focusing on those
aspects relevant to the work in the balance of this chapter.
5.1.1
Supply Models
Supply models represent the public transport network itself, including the various services
on the network and the physical infrastructure for pedestrian access and egress to and from
these services. Transport networks are typically represented as graphs – data structures
composed of nodes and edges, or links, that have an extremely wide set of applications in
many fields beyond transport analysis (e.g. Ahuja et al., 1993). The two most common
54
representations of public transport supply are line-based and run-based, where the latter is
more granular in the time dimension (Nuzzolo, 2003).
Line-Based Supply Models
Nguyen and Pallottino (1988) and Spiess and Florian (1989) describe and use the line-based
model of public transport supply in their seminal works on public transport assignment. They
represent the network with two distinct subgraphs – one representing the various transport
services and the other representing the pedestrian infrastructure. Figure 5-1 illustrates this
supply model with an example which includes some aspects of the station environment, such
as the entrance and the exit, with walking links to and from the platform. In this example,
Line 1 serves Station A, B, and C, whereas Line 2 bypasses Station B on the way from A to
C.
Service
Nodes
Line 2
Service
Links
Line 1
Alighting
Links
Boarding
Links
Platform
Node
Walking
Links
Entrance
Node
Exit
Node
Station A
Station B
Station C
Figure 5-1: Example of line-based representation of public transport network
The service subgraph is the union of a set of graphs representing each of the network’s
lines. Each line, or service pattern, is represented by a series of nodes and links describing
the stopping pattern of that service. The service nodes for a given line indicate which stops
that line serves. The time or cost associated with a service link connecting a pair of service
nodes indicates the time or cost of traveling on that line between the stops connected by that
link. Each line also has certain attributes which can include the name of the line, frequency
of service, the capacity of the vehicles on that line, the operating company, etc.
The pedestrian subgraph represents the physical aspects of the network that are used to
access and exit the transport services. The nodes in this graph represent locations, including station entrances, exits, ticket halls, and platforms. The links in this graph represent
pedestrian facilities (e.g. corridors, escalators, and stairs) between these locations.
The two subgraphs are connected by boarding links and alighting links at each stop. The
time or cost of a boarding link includes the assumed or average waiting time for passengers
55
boarding that service. In some cases it is assumed that passengers arrive at the service
randomly and that the service runs at perfectly even intervals, implying that the average
passenger waiting time is half the headway (the headway is the reciprocal of the frequency)
(Spiess and Florian, 1989).
It should be noted that in this type of model, the attributes of each part of the network
are assumed constant over a certain interval of time. It is possible for attributes to vary over
time, but such variation is represented with a sequence of fixed time intervals with constant
attributes. This is explained further later in this section.
Run-Based Supply Models
Nuzzolo and Crisalli (2004) present a good review of run-based supply models and their
applications. The primary difference between these models and the line-based models is
that run-based models represent points in time explicitly. The graphs for each line (service
pattern) are decomposed into graphs for each run (scheduled service) on that line. The
nodes in these run subgraphs indicate the time at which the run is scheduled to be at the
given location. This representation demands that the nodes in the pedestrian subgraph have
a temporal dimension as well. The OD estimation of this chapter does not require such
a highly granular temporal representation, so this discussion is postponed until Chapter 6
which does have such requirements.
5.1.2
Paths and Path Choice Models
Path (or route) choice models describe how passengers identify, evaluate, and choose paths
through the network from their origins to their destinations. The representation of paths in
the network depends on the network itself. Line-based supply models facilitate frequencybased path representations while run-based supply models facilitate schedule-based path representations. While any path through a transport network has temporal components (e.g. the
duration of a trip), the primary difference between these two types of paths is the degree
to which specific points in time, rather than time intervals, are represented. This section
describes frequency-based paths and path choice models. Schedule-based paths are discussed
further in Chapter 6, along with run-based supply models.
Frequency-Based Paths
Nuzzolo (2003) reviews some of the literature on frequency-based path choice models. In
this type of model, a path on the public transport network is evaluated with respect to
the frequencies of the services used on that path, as well as other attributes. The primary
relevance of frequency is that it is inversely proportional to waiting time (though the precise
relationship between frequency and waiting time depends on certain aspects of passenger
behavior). This framework accommodates walking links by representing them as services
with infinite frequency (and thus zero waiting time).
Given a line-based representation of the network, frequency-based paths are typically
identified via graph-based algorithms for finding the shortest path (or paths) according to
some criterion (Prashker and Bekhor, 2004). Common algorithms for finding shortest paths
56
are Bellman-Ford or Dijkstra (Bertsimas and Tsitsiklis, 1997). The total cost of a path is
typically modeled as the weighted sum of the time (or cost) of its constituent links, and may
be expressed in units of monetary cost or actual or weighted time. The cost of each link is
determined by the attributes of that link (e.g. travel time, waiting time, and walking time)
and a set of weights for those attributes that express user preferences. These weights can
be considered relative monetary values of time (VOT) (cf Small and Verhoef, 2007, Chapter
2) for different components of a public transport trip. Wardman (2001) reviews a range of
findings on travel time valuation.
Ben-Akiva et al. (1984) proposed the path labeling approach by which multiple different
sets of weights are used to identify multiple different shortest paths. An example of such a
labeled set of weights would be one that finds the path with the fewest interchanges.
Frequency-Based Hyperpaths
The type of model described above has (at least) one serious drawback. It assumes that
passengers identify paths in which they select only a single line to board from a given stop
or platform, whereas in reality they may wait at a boarding location and make decisions
about how to travel depending on which line a vehicle comes first. This is referred to as
the common lines problem. Spiess and Florian (1989) treat this problem by describing a
more sophisticated strategy on the part of the passenger. They propose that passengers
use optimal strategies to minimize the total expected travel cost. With such a strategy,
passengers select, at each boarding location, an attractive set of lines which they are willing
to board. Passengers then board, in a stochastic process, whichever of those lines departs
first. Their probabilistic path through the network is thus a function of the optimal strategy.
Nguyen and Pallottino (1988) develop the same idea in a graph-theoretic context. They
describe hyperpaths, the probabilistic superpositions of multiple paths through the network,
which result from the application of the strategies described by Spiess and Florian (1989).
The attributes of a hyperpath (e.g. travel time, wait time, total cost) are the respective
expectations of the attributes of the constituent paths, weighted by the paths’ relative frequencies. Both sets of authors describe an efficient algorithm with which to find the shortest
(i.e. least expected cost) hyperpath from an origin to a destination.
This formulation and solution algorithm are extremely elegant, if not completely realistic,
and the reader is encouraged to consult the original references for a more detailed presentations. Hyperpaths have found wide application in the field of public transport modeling.
For example, they are implemented by two popular transport modeling software packages,
EMME/2 and TransCAD.
Random Utility and Discrete Path Choice
Path Choice models describe how passengers choose between a set of identified paths (or
hyperpaths). Prashker and Bekhor (2004) provide a detailed review, including simple simulations, of a wide range of path choice models. The simplest model for path choices is
a deterministic one – that passengers choose only the single path with the least expected
cost from their origin to their destination. Models that allow for probabilistic choice between multiple paths derive primarily from random utility theory, for example as described
57
by Ben-Akiva and Lerman (1985).
According to random utility theory (in the context of path choices), the utility of each
path for each passenger is assumed to be a deterministic quantity, and passengers are assumed
to choose the single path with the highest utility (or least disutility, as the case may be).
However, the utility of each path to each user cannot be measured directly, nor can the model
account either for all attributes of each path or the preferences of each user. The utility of
the kth path to a given user is considered to be a random variable Uk , with a deterministic
component Vk and a random component εk , related by the equation
Uk = Vk + εk .
(5-1)
For the case of paths through a public transport network, Vk is estimated as the weighted
path time or cost as discussed above. Because each passenger chooses the path with the most
utility (as he or she perceives it), the fraction of passengers that choose each alternative
depends on the distribution of εk . The reader is referred to Prashker and Bekhor (2004) for
details on the different path choice models (and extensions thereof) that result from different
assumptions on εk . One of the most common assumptions, that εk are identically and
independently distributed (iid) Gumbel variables, results in the Multinomial Logit (MNL)
model. In the MNL, the probability of a passenger choosing path k (out of K alternatives)
is given by the equation
e Uk
.
(5-2)
Pr(pathk ) = P
Ui
i∈K e
The MNL is easy to use, but suffers from at least one significant limitation for path
choice modeling. The independence of irrelevant alternatives (IIA) property, which can be
interpreted as a failure to account for similarities between alternatives, produces unrealistic
path choice probabilities under some circumstances. This is a particular problem in the
presence of multiple paths with overlapping segments. Prashker and Bekhor (2004) explore
and discuss this issue in detail. Nevertheless, this model was used by Guo (2008) to model
path choices of passengers in the London Underground, a network with multiple possible
(and overlapping) paths for many of its OD flows.
5.1.3
Assignment Models
Assignment models, narrowly defined, depend on supply and path choice models to estimate
the utilization of each portion of the network, given demand. Line-based supply models and
frequency-based path choice models result in frequency-based assignment, as discussed in this
section. Run-based supply models and schedule-based path choice models result in schedulebased assignment, as discussed in Chapter 6. In the former, the results of the assignment
are estimated at the level of a certain piece of the network over a certain interval of time.
In the latter, results are reported for individual trips or vehicles at different points in time.
Aside from this distinction, Nuzzolo (2003) categorizes assignment models along the
following dimensions which are often used to characterize assignment models.
Deterministic vs. Stochastic Path Choice Models – as discussed above, whether passengers are assumed to choose paths deterministically, according to observed path at58
tributes, or probabilistically depending on observed and unobserved path attributes
and personal preferences.
Static vs. Dynamic – the granularity with which time is represented. Static models assume all attributes of the network and levels of demand and utilization are constant
over the period of interest. In dynamic models, the period of interest is broken up into
smaller intervals, between which the attributes of the network and levels of demand
and utilization can vary.
Congested vs. Uncongested Network – whether levels of demand and utilization affect
the performance of the supply. In a model which assumes no congestion effects, the link
costs in the network (e.g. walking times, waiting times, travel times) are independent of
the number of passengers assigned to each link. In a model which allows for congestion
effects, the link costs are a function of the assigned volume. This can result in internally
inconsistent results where, for a given link, the number of assigned passengers does not
correspond to the link cost used in the assignment. As a result, it is typically necessary
to take an iterative approach to finding a point of equilibrium where link costs, path
choices, and assigned volumes are internally consistent.
Congestion, Capacity, and Equilibrium
Clearly, many different types of assignment models are possible. Even for a selected point
in the dimensions described above – for example a static frequency-based model with deterministic path choices on a congested network – there are many possible ways to model
the causes and effects of congestion. One of the causes of congestion in public transport
networks as perceived by passengers is vehicle capacity. When vehicles are full, passengers
waiting to board will be delayed.
Spiess and Florian (1989) and Nguyen and Pallottino (1988) describe early approaches
to finding equilibrium in a frequency-based assignment model with deterministically selected
hyperpaths when link costs are monotonic functions of assigned volume. The literature in
this area since their work is extensive; a few examples are presented here. Cominetti and
Correa (2001) use a simplified bulk queueing model to model congestion effects in a frequencybased assignment model, and find the resulting equilibrium. Kurauchi et al. (2003), Bell and
Schmocker (2004), and Cepeda et al. (2006) present different ways to model the capacity
constraints of public transport vehicles, for example using absorbing Markov chains, and
the resulting congestion effects. Schmocker et al. (2008) extend some of this work into a
quasi-dynamic context that is more granular in the time dimension. Schmocker and Bell
(2009) use these models to analyze congestion on the London Underground.
5.2
OD Matrix Estimation Literature Review
The literature on OD estimation methods is quite rich. Cascetta and Nguyen (1988) provided
an early synthesis and survey of the field and Abrahamsson (1998) provides a somewhat
more recent and thorough review. This section is not intended to be a complete review of
59
the literature, but rather to discuss the various approaches considered and/or tested for this
particular application to the Overground.
Many methods for OD estimation are expressed in terms of finding the “best” OD matrix
that corresponds, via an assignment model, to the given link flows. Most approaches reviewed
here have been formulated as mathematical optimization problems. The difference between
the various formulations rests in how “best” is defined (be it in isolation or with respect to the
prior estimate or seed matrix) and whether the given link flows are viewed as deterministic
constraints or as approximate targets to be matched as closely as possible.
In this discussion, the term ‘link’ has very general meaning. Specifically, it refers to any
element of a transport network than can be modeled as an edge in a graph-based model.
This includes boarding and alighting of public transport services as well as walking or riding
between points in the network, as in the assignment models described above. It also includes
entry into or exit from the system at certain points, as a station gateline can be modeled as
a link between points outside and inside the paid area of the station.
It should be noted that the differences between various OD estimation methods are
largely orthogonal to the differences between the types of assignment models described in
the previous section. For example, the same OD estimation method can be used to estimate
static or dynamic OD matrices, depending on whether the associated assignment model
is itself static or dynamic. The OD estimation methods depend on the outputs of some
assignment model but are not specific with respect to how exactly that assignment model
works. The caveat to this is that when the assignment model includes congestion and thus
requires equilibrium, the same is required of the OD estimation method, as discussed later
in this section.
Section 5.2.1 presents a trivial OD estimation example to develop intuition around the
general problem of OD estimation. Section 5.2.2 reviews many of the methods that have been
proposed to solve the problem. Section 5.2.3 discusses the results of some simple simulations
that were conducted to test the properties of some of these methods.
5.2.1
OD Estimation Example
Figure 5-2 presents a trivial example of the OD estimation problem concerning a railway
line with four stations, A through D, with service only in the A → D direction. The loads
on the three links of this line, A → B, B → C, and C → D, are known to be 5, 10, and
5 passengers, respectively. In this network, the assignment model is trivial. This example
does not include a seed matrix.
The figure illustrates two OD matrices that are feasible solutions to the OD estimation
problem. The first solution is the trivial solution where the flow on each link corresponds
to an OD flow of the same number of passengers traveling only on that link. This is the
solution with the maximum number of passengers, 20, and the shortest trip lengths. The
second solution minimizes the number of passengers, 10, by maximizing the trip lengths.
In this example, the first solution has twice as many passengers as the second. Any
convex combination of these two solutions is in fact a solution to the stated problem and
will have a total number of passengers between 10 and 20. Naturally, in any solution, the
total number of boardings or alightings is equal to the total number of passengers, and the
respective locations of some of the boardings and alightings will depend on the solution OD
60
Load = 10
Load = 5
A
Train
Loads
Load = 5
B
C
D
OD Solution 1: 20 Trips
5
+5
10
OD
Flows
5
+10
+5
-5
-10
-5
Boardings &
Alightings
OD Solution 2: 10 Trips
5
+5
OD
Flows
5
+5
+5
-5
-5
Boardings &
Alightings
Figure 5-2: Example OD estimation problem
matrix. Any feasible solution will have 5 boardings at station A and 5 alightings at station
D.
This example illustrates the following for the general OD estimation problem in which
flows are given for an arbitrary set of links in the network.
• The OD matrix estimation process determines the estimate of the total number of
passengers.
• The OD matrix estimate determines the estimate of boardings and alightings at each
station.
• Generally, the given link flows do not uniquely determine the boardings and alightings.
Terminals present a special case, where the link flow departing a terminal determines
the number of boardings, and the link flow arriving a terminal determines the number
of alightings.
• A seed matrix that offers some information about the true OD matrix is important,
because there are infinitely many OD estimates that can match the given link flows.
These general attributes are important for understanding much of the balance of this
chapter.
5.2.2
OD Estimation Methods
Iterative Proportional Fitting
Iterative Proportional Fitting (IPF, also Furness or Fratar or Bregman’s balancing method)
is a simple and widely used iterative procedure for expanding or adjusting a seed matrix to
61
exactly fit one or more sets of marginal totals, e.g. total entries and exits at each station
(Lamond and Stuart, 1981; Ben-Akiva et al., 1985; Ben-Akiva, 1987). These marginal totals
are “complete” in that every OD flow contributes its full volume to exactly one element of
each set of (entry and exit) marginal totals. Thus, this method takes the total volume of
demand (i.e. sum of the OD matrix) as known, equal to the sum of one of the marginals
(e.g. sum of station entries).
The IPF method has been used for the last decade or so by the London Underground
(Maunder, 2003) to estimate dynamic OD matrices at the 15-minute level by scaling mailback passenger surveys to meet marginal totals of entries and exits (estimated from gateline
and manual counts) and age, trip purpose, and ticket type (from a separate in-person survey).
Recent applications have used IPF to estimate time period level OD matrices from AFCbased seed matrices and entry/exit totals for urban rail networks. Specifically, Wilson et al.
(2008) and Chan (2007) for the London Underground and Zhao et al. (2007) and Zhao (2004)
for the Chicago Transit Authority rail network.
These applications of IPF can be seen as special cases of the general OD estimation
problem, in which the set of links on which flows are given is all entry and/or exits to
the network. In more general contexts, the measured link flows do not necessarily constitute
complete marginal totals because a given OD flow can be assigned to multiple link flows, and
so IPF is not applicable. Note that unlike the cited applications, the total volume of demand
in the general case (i.e. given flows on an arbitrary set of links) is considered unknown and
is determined by the OD estimation process.
Entropy Maximization and Generalized IPF
Van-Zuylen and Willumsen (1980) proposed to estimate an OD matrix by maximizing the
“entropy” function (from information theory) of the prior (i.e. seed) and estimated OD matrices subject to the constraint that the estimated OD matrix, assigned to the network,
reproduces the given link flows exactly. In this formulation, a given OD flow can be assigned
to the network such that it contributes probabilistically to multiple link flows. Despite the
fact that the Entropy Maximization (EM) method is formulated as a complex non-linear
optimization problem, it can be easily solved by a simple iterative technique (Lam and Lo,
1991). On the other hand, it is possible for inconsistencies in the link flows to render this
problem infeasible. This method was used by Wong and Tong (1998) to estimate timedependent OD matrices (with a schedule-based assignment model) for the Hong Kong MTR
metro system with high accuracy given a high-quality prior OD matrix.
The simple IPF method discussed previously is known to minimize a certain error function of the prior and estimated OD matrices subject to the constraints of the known marginal
totals (Ben-Akiva et al., 1985). The IPF error function is simply the negative of the entropy
function maximized by Van-Zuylen and Willumsen (1980). In addition, a generalized version of IPF (GIPF, also Generalized Iterative Scaling), which also allows for probabilistic
assignment, has been studied by Darroch and Ratcliff (1972) and shown to maximize the
same entropy function. In that sense, IPF is a special case of EM.
Paramahamsan (1999) and Maher (1987) have studied the EM method and found that,
if the network structure and selection of link flows are such that the total volume of demand
is known and constant (e.g. the case for which the IPF method is applicable), then uniform
62
scaling of the seed matrix will not affect the estimates of the final OD matrix. In the general
case, when total demand is not known, they find that uniform scaling of the seed matrix
will affect the final OD estimates. These are very important properties to consider, in fact
they should be cause for concern, when using a fractional seed matrix estimated from a AFC
system used by only a sample of passengers (representative as that sample may be).
Information Minimization
Van-Zuylen and Willumsen (1980) also proposed to estimate an OD matrix by minimizing an “information” function (also from information theory) of the prior and estimated
OD matrices subject to the flow constraints. The only difference between the Information
Minimization (IM) and EM methods is the objective function in the resulting optimization
problem. They also show that IM can be derived by applying EM to the link flow volumes
themselves rather than to the OD flows directly. The IM formulation can be solved via the
same algorithm developed for EM with one slight modification (Lam and Lo, 1991). It is
susceptible to the same link flow inconsistency issues as EM.
Paramahamsan (1999) and Maher (1987) also studied IM and showed that, unlike EM,
the final OD matrix estimate is not affected by uniform scaling of the seed matrix. This is
a desirable property when using a fractional AFC-based seed matrix and a set of link flows
such that total demand is not held constant.
Lam and Lo (1991) compared the performance of IM and EM using “complete” information on origin, destination, and path choice from over 13,000 roadside surveys of drivers in
the AM and PM peak periods on a road network with 23 zones and 328 links in Shenzen,
China. They used both methods to estimate the AM peak OD matrix in a range of scenarios
defined by (i) varying the number of links with given flows (from one to forty), (ii) assigning
based on all-or-nothing or observed link choice proportions, and (iii) using the PM peak
matrix as the prior OD estimate, using the transpose of the PM peak matrix as the prior,
or using no prior. Their primary conclusions were as follows.
• The better the prior OD estimate and the more link flows given, the better the results
under IM and EM.
• IM outperformed EM with a good prior OD estimate, but lacking a prior estimate EM
outperformed IM.
• The simplistic all-or-nothing assignment model did not introduce substantial additional
error into the results, especially in the presence of a good prior OD estimate.
• Both methods underestimated total demand but by less than 5% and 7% in all IM
and EM scenarios, respectively. With a good prior OD estimate and the observed path
choice proportions this underestimate was less than 2% for both methods.
(Constrained) Generalized Least Squares
Cascetta (1984) proposed to estimate OD matrices using the familiar framework of Least
Squares (LS) regression (Greene, 2007) by taking advantage of the fact that, for a given
63
assignment, the link flows are a linear combination of the estimated OD flows. The use of
Generalized Least Squares (GLS) is also proposed, to account for variance and covariance
of the model’s error terms. The primary benefits of this approach are that (i) it allows the
estimated OD matrix to match the given link flows only approximately, (ii) it has known
statistical properties, and (iii) it can account for varying statistical accuracy of the inputs.
Bell (1991) extends this approach to include (necessary) non-negativity constraints on the
OD estimates.
Unlike traditional linear regressions, this approach does not allow an intercept (constant)
term in the model specification. Because linear regressions require error terms to be of zero
mean, the lack of an intercept implies that the seed matrix is an unbiased estimate of the
true matrix. This is not appropriate in the context of an AFC-based fractional seed matrix
that is known to be a lower bound on the actual OD matrix. It should be possible to extend
the GLS approach to deal with this bias, for example by adding constant terms to the model,
but this confuses the interpretation of the model results and is beyond the scope of this work.
Maximum Likelihood Estimation
Maximum Likelihood Estimation (MLE) is a very general and powerful type of statistical
estimation with many desirable statistical properties (Greene, 2007). It is used, for example,
to estimate discrete mode-choice models from household transportation surveys (Ben-Akiva
and Lerman, 1985). In the context of OD estimation, the benefits of MLE are that it allows
for flexibility in the types and accuracy of inputs, explicit assumptions about the degree and
type of randomness in any of the data, and full flexibility of functional form.
For example, Hsu (1985), Ben-Akiva et al. (1985), and Ben-Akiva and Morikawa (1989)
propose and test, on real-world data, a number of MLE formulations assuming Poisson
distributed OD flows and different models of bias in the prior OD estimate. Their problems
are similar to those solved by IPF in that they have a seed matrix and complete marginal
counts at the entries and/or exits of the system. However, Ben-Akiva and Morikawa (1989)
are able to explicitly estimate the bias in the prior OD estimate as a function of trip length
as well as seasonal and trip-purpose characteristics, something impossible to do with IPF.
On the other hand, some MLE formulations are equivalent to other methods listed here.
Hsu (1985) proves that the Poisson MLE model with multiplicative bias parameters on all
origins and destinations yields equivalent results to IPF. The GLS methods described above
are known to be equivalent to MLE when it is assumed that all OD flows come from a
multivariate normal distribution (Cascetta, 1984).
The advantages of MLE seem to be clearest when there is a strongly-held belief about
the nature of the randomness in the problem or the functional form of the model (e.g. type
of bias in prior OD estimate). However, the more complex the MLE model, the harder it
can be to solve in real-world applications. For example, the complex MLE model proposed
by Lo et al. (1996) can have a non-convex objective function, requiring the development
of a custom algorithm that is still not guaranteed to find a global optimum solution (Lo
et al., 1999). It is worth noting here that some of these same authors choose instead to
use the much simpler Entropy Maximization method described above in subsequent work
on complex real-world problems such as the estimation of combined OD matrices for Hong
Kong’s complex multi-modal public transport network (Wong et al., 2005).
64
Gradient Descent
Spiess (1990) takes an approach that is somewhat different from the others discussed here,
in that it seeks only to minimize the difference between the given link flows and the link
flows implied by the estimated OD matrix. It depends on a particular choice of optimization
algorithm – in this case the gradient method (also known as steepest descent) – to change the
prior OD matrix as little as possible. This method was designed with scalability in mind, as
other methods apparently could not handle large real-world networks at the time. This has
become substantially less of an issue with the expansion of computing power in the decades
since.
The primary reason this method is discussed here is that it was implemented as part
of the commercial transportation modeling software package EMME/2, updated versions of
which are used by Transport for London for strategic modeling of London’s public transportation network (Warner, 2010). Current versions of EMME/2 may have maintained the
implementation of this OD estimation method, in which case it may be possible for Transport
for London to estimate OD matrices without the purchase or development of any specialized
software.
Multiple Path Matrix Estimation
Nielsen (1998) proposed a heuristic approach to estimating OD matrices, called Multiple
Path Matrix Estimation (MPME), and used it for OD estimation of large urban traffic
networks. It is similar to some of the other methods described here, but heuristic in the
sense that it does not optimize any explicit objective function per se, and does not have
well-defined statistical properties. More recently, Nielsen et al. (2008a) used MPME to
estimate dynamic OD matrices of a large urban railway network in Copenhagen, Denmark,
using complete train loadweigh data and existing survey-based OD matrices. This method is
available as part of the commercial transport modeling software package TransCAD (Caliper
Corporation, 2007).
The Total Demand Scale
The Total Demand Scale (TDS) is not an OD estimation method per se, but rather a
measure proposed by Bierlaire (2002) to characterize the ambiguity inherent in a specific
OD estimation problem instance. In short, it is proposed to find two OD estimates with the
minimum and maximum total demand, respectively, that still satisfy the flow constraints
(and of course have only non-negative values). The range between the minimum and the
maximum provides an indication of how much the total estimated demand can vary, and
thus can provide insight into the overall effect of the prior OD estimate. This measure is
easily estimated using well-known linear programming (i.e. linear optimization) algorithms.
OD Estimation Under Congestion and Equilibrium Models
The formulations for the OD estimation methodologies reviewed here are generally expressed
in terms of fixed path or link probabilities for each OD flow. When congestion and capacity
65
constraints are considered using equilibrium assignment models, this approach can yield
internally inconsistent results.
The widely accepted approach to OD estimation under equilibrium assignment, for example as proposed by Nielsen (1998) and Cascetta and Postorino (2001), is to use an iterative
bi-level estimation process. In such a process, each iteration consists of two steps. First,
the OD estimate is held fixed and the equilibrium path or link probabilities are estimated
using the assignment model. Second, the path or link probabilities are held fixed and the
OD matrix is estimated using one of the above methods. Such iterations are repeated until
the OD estimate and path or link probabilities converge.
5.2.3
Simulation of OD Estimation Methodologies
A number of these OD estimation methods, including Entropy Maximization, Information
Minimization, Least Squares, and Gradient Descent, were tested using simulations of a very
simple network. The narrow goal of these simulations was to test the sensitivity of each
method to different Oyster penetration rates.
In each simulation, a ‘true’ OD matrix is randomly generated and ‘true’ link flows are
derived from the true OD matrix and the network structure. Next, an Oyster penetration rate
is randomly generated for each OD flow. The ‘Oyster’ seed matrix is generated by multiplying
each OD flow in the true OD matrix by the respective simulated Oyster penetration rate.
Each OD estimation method is then used to estimate an OD matrix from the true link flows
and the sampled seed matrix, and the results are compared with the true OD matrix.
In addition, each OD estimation method was tested on a seed matrix uniformly scaled
in two different ways. First, the seed matrix was uniformly scaled so that the total number
of trips was equal to the total number of trips in the true OD matrix. This is intended to
simulate a situation in which, somehow, the total volume of trips is known a priori and this
knowledge is used to adjust the seed matrix before the OD estimation process. Second, the
seed matrix was uniformly scaled so that the sum of the seed matrix is one (i.e. it is reduced
to a pure multinomial probability distribution over the OD flows). In this context, the seed
matrix contains information only about the distribution of trips in the network, and not the
volume of trips.
The finding from these simulations is that, as expected, the Information Minimization
method is indeed unaffected by uniform scaling in the seed matrix. That is, it produced the
same result regardless of whether the seed matrix was scaled up, down, or not at all. All
other methods tested were sensitive to such scalings. Their performance generally improved
when the seed matrix was scaled up to match the total volume in the true OD matrix, and
degraded when the seed matrix was scaled down to a probability distribution.
5.3
OD Estimation Strategy for the London Overground
The many available assignment models and OD estimation methods cover a wide spectrum
of complexity and sophistication. The strategy developed for the purposes of this application
is quite simple, primarily as a result of the following circumstances which are described in
further detail throughout the balance of this section.
66
• The required time scale for OD estimation is the time period level. For example, the
three hour AM Peak from 07:00 to 10:00.
• High confidence is expected to be placed in the measured link flows, be they from
loadweigh data or manual counts.
• The shape of the Overground network is such that for any trip assumed to have used the
Overground, there is never more than a single reasonable path through this network.
• It is assumed that for most passengers, the choice of path (with respect to using the
Overground or not) is largely insensitive to different (but reasonable) assumptions
about how congestion and passenger preferences affect the choice among path alternatives. This assumption likely has some truth to it, but is adopted primarily as an
engineering simplification.
These simplifications and other more specific derived assumptions allow the development of
the assignment model and OD estimation methodology described in the following sections.
A subsequent sensitivity analysis tests how sensitive the assignment model is to violation of
most of these assumptions.
5.3.1
Assignment Model for the London Overground
This section describes in detail all aspects of the proposed assignment model. In the language
of assignment models developed above, the proposed assignment model is a static frequencybased model that does not account for congestion and addresses the common lines in a
limited way without the traditional hyperpath-based approach. The purpose of the model is
to relate OD flows to link flows to support the OD estimation process. This model is for the
most part derived from specific assumptions about passenger behavior, but is also a product
of certain engineering simplifications.
Congestion and Capacity
It is assumed that for most passengers, the choice of path (with respect to using the London
Overground or not) is insensitive to the effects of congestion, including vehicle capacity
constraints. From the perspective of Overground managers, this is a conservative assumption
because the likely effect of congestion would be to divert passengers from the highly-congested
London Underground to the less congested Overground.
Static and Line/Frequency Based
Because OD matrices are desired at the time period level, this work takes a static approach to
line- and frequency-based assignment as reviewed by Nuzzolo (2003). That is, the network
is described in terms of infrastructure (e.g. stations, platforms, etc) that is connected by
public transport lines running in fixed service patterns at specific frequencies. Nguyen and
Pallottino (1988) and Nuzzolo (2003) provide extensive detail on this type of representation,
including the specific graph structures to use.
67
The model is static in the sense that service and demand levels are assumed constant
over the entire period of interest. This is reasonable in terms of service levels because the
time periods over which OD matrices will be estimated are the same time periods used
for scheduling, and reasonable in terms of demand because of the assumption regarding
congestion and capacity.
Passenger Arrival Behavior and Waiting Time
It is assumed that the times of passenger arrival at stations are independent of any published
timetable at headways (intervals between services) of ten minutes or less, but are influenced
by the timetable at longer headways. This assumption is operationalized by the expression
for average waiting time W as a function of headway H and a threshold T shown in Figure
5-3 and Equation (5-3). The “random incidence threshold” T is the headway below which
passengers arrive randomly and thus should wait on average half the headway, assuming
even headways1 (Osuna and Newell, 1972). Beyond this threshold, behavior changes but no
assumption is made regarding the change in behavior other than to say that the average
waiting time will be as shown in the second case of Equation (5-3). This function was used
by Casello and Hellinga (2008), with T = 10.
(
H
,H ≤ T
(5-3)
W (H) = 2 T (1− H )
T− e T
,H > T
2
It is a property of this function, illustrated in Figure 5-3, that the upper bound on
waiting time is the value of the random incidence threshold, i.e. W ∈ (0, T ), ∀ H > 0. This
function is adopted as an engineering simplification; more complex models exist and could
be used. This simplification is thought to be reasonable because, as discussed in Chapter
6, the average waiting time (with respect to the timetable) on the London Overground was
found to be approximately 10 minutes or less over the entire network at all times of day.
1
See Chapter 6 for a detailed discussion of the relationship between headways, passenger behavior, and
waiting time.
68
10
8
6
4
Random Incidence Threshold = 10
H
2
Average Waiting Time (min)
●
2
H
(1−10
)
0
10 − 5e
0
10
20
30
40
50
60
Headway (min)
Figure 5-3: Waiting time as a function of headway
Indifference between Interavailable Services
It is assumed that passengers are indifferent between distinct but interavailable services
(i.e. common lines) with identical stopping patterns on a given corridor. For example, on a
line with a trunk segment and two branches, passengers traveling on the trunk are indifferent
between services bound for either branch. Also, on a corridor of consecutive stations all
served by multiple providers, passengers are indifferent between the different services.
This is a simplified version of the optimal strategies assumption made by Spiess and
Florian (1989). It allows the use of a straightforward augmentation of the network structure
to faithfully represent this indifference without depending on formal hyperpaths and related
algorithms. The crux of this augmentation is the following. Between each pair of consecutive
stations, a new “composite service link” is added for each possible combination of services
that connect those two stations. Each link represents the superposition of a possible set of
services that a passenger could decide to use to travel between the pair of stations. These
links are analogous to the “attractive set” in the model of Spiess and Florian (1989).
The service frequencies, running times, and fractional assignment of passengers for these
new composite service links are determined according to the model of Spiess and Florian
(1989). The service frequency for each new link is simply the sum of the frequency of the
combined services. It is assumed that the headway of the combined services is even and equal
to the inverse of the combined frequency.2 Since it is assumed that passengers are selecting
between these services randomly, it is also assumed that passengers arrive randomly and
so always experience a waiting time of half the combined headway. The running time for
each new link is the frequency-weighted average running time of the services making up that
link. When a number of passengers is assigned to one of these composite service links, the
fraction of passengers assigned to the individual service links is determined by the respective
2
This assumption, that the headways of the combined services is even, is coarse but, nevertheless, a
common feature of frequency-based models.
69
frequency shares.
This augmentation is illustrated in Figure 5-4. In this example, the London Underground
(LU) and London Overground (LO) both serve the link between North Wembley and Willesden Junction with a single service pattern each, with equal running times on this link. The
Underground service is 6 tph (a 10 minute headway), so according to the above waiting time
model passengers experience an average waiting time of 5 minutes. The LO service is 3
tph (a 20 minute headway), with an average waiting time of 8.1 minutes (as per the model
described above). This results in a single composite service link with a combined frequency
of 9 tph, a constant headway of 6.66 minutes, and an average waiting time of 3.33 minutes.3
33.3% of passengers assigned to this link will be assigned to the Overground service, with
the balance going to the Underground service.
N. Wembley
LU: 6 tph
WT = 5 min
LO: 3 tph
WT = 8.1 min
Combined: 9 tph
WT = 3.33 min
Frequency Splitting:
LO gets 33%
LU gets 66%
W. Hampstead
Willesden Jn
S. Hampstead
Paddington
Figure 5-4: Illustration of network augmentation
This example also illustrates how this model reasonably captures overall passenger behavior, depending on passengers’ eventual destinations. For passengers traveling from North
Wembley to Paddington, the shortest path will not use the new composite service link because to do so would necessitate an additional waiting and boarding at Willesden Junction
to continue on to Paddington. These passengers are better off on a path containing only the
Underground-only link. Likewise for passengers traveling to South Hampstead, for whom
the shortest path would include the Overground-only link.
Passenger Preferences and Path Choice
It is assumed that for most passengers, the choice of path (with respect to using the London
Overground or not) is largely insensitive to different (but reasonable) assumptions about
3
It is in fact impossible to combine two even headway services of 6tph and 3tph, respectively, into a single
9tph even headway service. This is an example of the types of approximations that occur in frequency-based
models.
70
how passengers choose among alternative paths. Nevertheless, for each OD flow, different
models for passenger preferences are used to identify up to three possible lowest-cost paths
and then apply a discrete choice model to predict the fraction of passengers choosing each
path. These methods are reviewed extensively by Prashker and Bekhor (2004) and Guo
(2008).
In this model, the cost of a path is equated with the generalized journey time of that
path. The generalized journey time (GJT) of a path is a weighted sum of the time of its
constituent links. The GJT weights on each type of link (e.g. walking, boarding, riding a
service) express passenger preferences. A range of different weighting schemes and values
are used within TfL for different purposes (Transport for London, 2009a; Guo, 2008; London
Transport, 1999). The following simple set of GJT weights has been selected, as prescribed
for analysis of the London Underground by the TfL’s Business Case Development Manual
(BCDM) (Transport for London, 2009a). These weights reflect the information available
in the RODS network representation and retain sufficient detail for the purposes described
here.
βInV ehicle = GJT weight for time spent riding (or dwelling) inside a transit vehicle.
βW ait = GJT weight for time spend waiting outside a transit vehicle.
βInterchange = GJT weight (in minutes) for number of interchanges.
βW alk = GJT weight for time spent walking.
Given a set of weights, the single lowest-GJT path is found using the Hao-Kocur shortest path algorithm (Hao and Kocur, 1992), but other algorithms such as Bellman-Ford or
Dijkstra’s (cf Bertsimas and Tsitsiklis, 1997) would work just as well. To identify multiple
alternative paths, the path labeling approach is adopted, in which the GJT weights are modified and the shortest respective paths are found (Ben-Akiva et al., 1984). Three labels and
respective sets of weights are used – one according to the BCDM, one to minimize travel
time, and one to minimize interchanges – as shown in Table 5-1.
Label
BCDM
MinTime
MinInterchange
βInV ehicle
1.0
1.0
1.0
βW ait
2.5
1.0
1.0
βInterchange
3.5
0.0
1,000
βW alk
2.0
1.0
1.0
Table 5-1: Labels and weights for identification of alternative paths
For each OD flow, the shortest path is found under the application of each label’s weights.
Duplicates are then removed, where two paths are duplicates if they visit the same stations
in the same order. For each remaining path, the GJT is calculated using the weights of
the BCDM label. The choice probabilities for each path are estimated using the simple
Multinomial Logit (MNL) model, which was used by Guo (2008) to analyze path choices on
the London Underground. According to the MNL model, for a given OD flow,
eGJTk
GJTi
i∈K e
Pr(pathk ) = P
71
(5-4)
where K is the set of available paths and GJTk is the GJT of the k th path.
Finally, any path with probability less than a certain “path probability threshold,” 10%,
is dropped and all path probabilities are re-normalized to sum to 100%. This is done to
prevent OD flows with only a very small likelihood of using the Overground from factoring
into the subsequent OD estimation process, since that process will be based on link flows
measured only on the Overground. This is effectively a convenient heuristic that attempts
to eliminate spurious artifacts of the above modeling assumptions.
Operator Aggregation
One feature of the RODS network representation is that each service line is assigned a specific
operator code. One operator code is assigned for the entire London Overground network.
These operator codes are used in the following two types of aggregation in the assignment
model. Both of these aggregations happen after the assignment process.
Operator links are the aggregation of all services by a given operator between a given pair
of adjacent stations. This operation is designed so that outputs of the assignment model
correspond to the given link flows, which will be used at the same level of aggregation in
the static time period level OD estimation context. For example, the London Overground
and the London Underground both provide service connecting the adjacent Richmond and
Gunnersbury stations. Under the described aggregation, the assignment model produces
results for two different operator links between these two stations. Only one of these links,
that of the Overground operator, will have corresponding link flows in the OD estimation
process (given the data available).
Operator clamps are a somewhat more subtle concept. The Oyster system allows passengers to interchange between services (of the same operator or different operators) without
conducting additional validation. OD flows in this work are defined by pairs of Oysterenabled stations, most of which contain at least one station outside the Overground network.
Since the goal is to estimate an OD matrix for a single operator, the assignment model must
provide a means by which to map end-to-end OD flows (i.e. first and last points of Oyster
transactions) to the OD flow on a given operator’s network (i.e. first and last stations at
which that operator’s services were used).
This process, referred to as “clamping” of OD flows, provides a “clamp” which describes
the “clamped” or “inner” OD flow entirely on the given operator’s network that would
be used by passengers traveling on the “unclamped” or “outer” end-to-end OD flow. For
example, the Overground clamp for the outer OD flow of Leyton (on the Underground
Central Line) to Camden Road (on the Overground North London Line) is Stratford (where
the two lines meet) to Camden Road, with a share of 100%. This means that all passengers
traveling from Leyton to Camden Road are predicted to interchange at Stratford to the North
London Line, and will be counted as part of the Stratford to Camden Road Overground-only
OD flow.
The clamped OD flow can be smaller than the unclamped OD flow if that clamp is along
a path predicted to be used by only a portion of passengers. For example, all passengers
from Wembley Central (on both the London Underground’s Bakerloo Line and Overground’s
Watford DC Line) to Oxford Circus (on the Bakerloo Line) are predicted to travel via Queen’s
Park (also on both lines). However, because the Bakerloo Line frequency is substantially
72
higher between Queen’s Park and Oxford Circus than between Wembley Central and Oxford
Circus, all passengers are predicted to be indifferent between the Bakerloo Line and the
Watford DC Line at Wembley Central. Those who, by chance, take the Watford DC Line
will transfer at Queen’s Park to the Bakerloo Line to continue their journeys. Since the
frequency at Wembley Central of the Bakerloo Line is twice the frequency of the Watford
DC Line, the Overground clamp for this OD flow is Wembley Central to Queen’s Park with
a 33% share. An algorithm for accomplishing this sort of computation is described in detail
in Appendix D.
Out-of-Station Interchanges
The RODS network representation includes walking links between stations that are near
each other but not directly connected. At the same time, the Oyster ticketing system allows
selective free “out-of-station interchanges” (OSI’s) wherein passengers validate when exiting
one station in the OSI pair and then validate again when entering the other. For a number
of reasons, these interchanges are not handled perfectly in the assignment model.
Unfortunately, the set of OSI’s in the RODS network representation is not perfectly
congruent with the set of OSI’s in the Oyster system. Furthermore, the assignment model
only records explicit entrances and exits, for a given OD flow, at the first station of entry
and last station of exit. This will be a source of error in the assignment model, and should
receive attention in the future.
Implementation and Outputs
The assignment model described here is implemented as a custom software package of nearly
3,200 lines of code developed in the widely-used free programming language Java (Sun Microsystems, 2009). This program, called ODNet, proceeds more or less as follows.
1. Read updated RODS network representation, including infrastructure and service patterns and frequencies.
2. Select service patterns and frequencies for a specific time period of interest (e.g. weekday
AM Peak).
3. Modify network model to reflect separate physical and service networks, and add boarding and alighting links to connect the two.
4. Determine the presence of interavailability and augment the network with additional
services and boarding and alighting links to reflect passenger indifference.
5. For each pair of Oyster-enabled stations, assign a single passenger on that OD flow to
the network and output link and clamp flows for the London Overground operator.
It is worth discussing here the effects on the network size and algorithmic performance
of the augmentation in step 3. The RODS network representation has 7,213 service links
for the AM Peak period. The augmentation adds 22,453 common service links, effectively
73
quadrupling the size of the graph representing the TfL rail network. This change has no
perceptible effect on the performance of the assignment algorithms used in step 4.
The last step of this process is appropriate only because congestion effects and capacity
constraints are not considered. Because each OD flow is treated separately and only a single
passenger is assigned, the resulting link flows can be interpreted as link probabilities for a
given passenger traveling on that OD flow. These link probabilities, for a given OD flow,
depend on
• the paths through the network identified for that OD flow,
• the probabilities of each path,
• the London Overground links along each path,
• the relative combined frequency share of Overground services on each link.
Clamp flows are estimated as part of the same process, and likewise interpreted as clamp
probabilities. These link and clamp probabilities, discussed in further detail in following
sections, are the crucial input from the assignment model into the OD estimation process.
Sensitivity Analysis
A number of scenarios were used to test the sensitivity of the assignment model to the various
assumptions described above. In each scenario, some aspect of the assignment model was
modified and the link and clamp probabilities were re-calculated and saved. For the sake of
this sensitivity analysis, two quantities are defined. The competitive market is the set of all
OD flows for which the assignment model predicts a positive probability of using the London
Overground. The captured market is the set of all OD flows of the competitive market after
being clamped to the Overground network. The size of each of these markets is simply the
sum of the respective market’s OD flows.
Figure 5-5 shows the results of the sensitivity analysis. The competitive and clamped
market sizes are based on a raw Oyster OD matrix estimated as the daily number of Oyster
journeys on each OD flow departing during the AM Peak averaged over all weekdays of
March, 2009. The Baseline scenario is as described in the preceding sections, using Weekday
AM Peak service patterns and frequencies. The scenarios tested are as follows, where each
is described with respect to the Baseline scenario.
• LU Congested (10%): To simulate the increase in perceived travel time caused by
congestion on the London Underground, running times on all London Underground
services are increased by 10%. This is a poor approximation of congestion, since it
assumes congestion does not vary spatially or temporally.
• LU Congested (25%): Likewise, increased by 25%.
• High Wait Cost: βW ait = 5.0.
• RI Threshold = 5 : The random incidence threshold in the waiting time function is set
to 5 minutes.
74
• RI Threshold = 30 : The random incidence threshold in the waiting time function is
set to 30 minutes.
• Path Threshold = 1% : The path probability threshold is set to 1%.
• Path Threshold = 20% : The path probability threshold is set to 20%.
• All-or-Nothing (GJT): A deterministic all-or-nothing (rather than stochastic MNL)
assignment is used, taking the single lowest-GJT path for each OD flow.
• All-or-Nothing (Time): A deterministic all-or-nothing (rather than stochastic MNL)
assignment is used, taking the single lowest-travel time path for each OD flow.
• No Common Lines: The assumption of indifference to interavailable services is disregarded, and no common line links are generated.
London Overground Competitive Market Size
London Overground Captured Market Size
20000
15000
10000
s
Li
ne
e)
on
m
om
C
o
N
Al
l−
o
r−
N
ot
ot
hi
hi
ng
ng
(T
i
(G
m
JT
)
20
%
=
or
−N
l−
Al
re
s
Th
h
h
Pa
t
Pa
t
Th
re
s
ho
ho
ld
ld
ld
=
=
1%
30
5
hr
es
IT
R
R
IT
hr
h
ig
H
ho
es
ho
ld
tC
W
ai
d
te
ge
s
=
os
)
(2
5
%
)
%
(1
0
LU
C
on
ge
s
te
d
Ba
on
C
LU
t
5000
se
lin
e
Oyster Journeys
25000
Horizontal blue and orange lines show the size of the London Overground’s competitive and captured
markets, respectively, in the baseline scenario
Figure 5-5: Sensitivity of London Overground Oyster-only competitive market size and
assigned trips
The assignment model does appear to be somewhat sensitive to the crudely simulated
congestion on the London Underground, moreso at higher levels of simulated congestion.
Even higher levels of simulated congestion would likely result in more drastic changes in
the market sizes. That said, the simulation of congestion here is rather crude in that it
assumes the congestion is spread uniformly across the entire London Underground network.
In reality, the Underground is most congested in Central London, where it does not generally
compete with the Overground.
The model appears to be generally insensitive to changes in GJT weights, the random
incidence threshold, and the path probability threshold. This adds to confidence in the model
75
because the variables tested in those scenarios are, in a certain sense, the most numerically
arbitrary. The assignment model is somewhat sensitive to the two All-or-Nothing scenarios,
but when passengers are assumed to take only the path that minimizes GJT, the captured
market size does not change appreciably. This also adds to confidence in the model because
it corresponds to modeling assumptions across TfL which hold that some weighted measure
of GJT is a more realistic determinant of path decisions than is total travel time. Note that
in the All-or-Nothing scenarios, the competitive market size and captured market size are
still different because of the randomness associated with interavailability.
Probably most importantly, the drastic change in the No Common Lines scenario, in
particular that the two markets are almost the exact same size, indicates the importance
of the assumption of indifference to interavailable services. This adds to confidence in the
model because it is believed by Overground management that this assumption is accurate
for certain Overground corridors.
The overall results of this sensitivity analysis are generally coincident with the assumption
that passengers using the Overground do not for the most part have reasonable alternatives,
and gives confidence that the assignment model itself is reasonable. With this confidence,
it becomes possible to use the formulation described in the next section to estimate OD
matrices for the Overground.
5.3.2
Information Minimization Matrix Estimation
Of the many available approaches to the OD estimation problem, the Information Minimization (IM) formulation proposed by Van-Zuylen and Willumsen (1980) appears most
appropriate for the circumstances faced by the London Overground. It is straightforward
and simple to implement (given the outputs of the assignment model), and is a methodological cousin to the Entropy Maximization (EM) and IPF methodologies long used by the
London Underground. As in Section 5.2, the term ‘link’ is used abstractly; it can refer to
boarding, alighting, riding, walking in a public transport network as well as entry into or
exit from the network.
In the Underground case, link flows are given at all entrances and exits to the network,
and so total demand levels are fixed. In the Overground case, link flows are given primarily
inside the network, and so total demand is a function of the OD estimation process. It has
been found that, when total demand is not fixed, EM is sensitive to uniform scaling of the
seed matrix (as will be the case when it is Oyster-based), but IM is not (Paramahamsan,
1999). Thus, IM is appropriate under the circumstances while being the OD estimation
method most similar to those already used for similar problems within TfL.
The rest of this section shows the explicit mathematical IM formulation for OD matrix
estimation proposed by Van-Zuylen and Willumsen (1980), and discusses several issues.
Formulation
Let
K = The set of links for which flows are available.
Vk = The observed flow on link k.
76
pkij = The proportion of trips from i to j that use link k. This assumes the existence of a
satisfactory assignment model which is used to generate pkij .
tij = The measured flow from origin i to destination j in the seed OD matrix.
Tij = The flow from origin i to destination j in the estimated OD matrix.
Using this notation, Van-Zuylen and Willumsen (1980) formulate the OD estimation
problem as follows:
XX
Tij S k
k
(5-5)
min
Tij pij log
Tij
V
t
k
ij
k∈K ij
where
Sk =
X
pkij tij , ∀k ∈ 1..K
(5-6)
pkij Tij , ∀k ∈ 1..K.
(5-7)
ij
subject to the flow constraints
Vk =
X
ij
Through a Lagrangean analysis, they find that the OD flow estimates
Tij = tij
Y
Xk
pk
ij
gij
!
(5-8)
k∈K
where
gij =
X
pkij
(5-9)
k∈K
and Xk , a function of the known inputs and the Lagrangean multipliers, can be found
through an efficient and simple iterative solution algorithm which is described in detail
by Lam and Lo (1991). This algorithm, as well as the integration of the various data
sources used in this chapter, was implemented in R, the free and open source statistical and
graphical programming language and environment (The R Project, 2009). The convergence
criteria for this algorithm were that Equation (5-7) be satisfied for each link to within ± 1%
(i.e. approximately, rather than exactly).
Considerations
For this approach, the seed matrix should be an average of several days or weeks of Oyster
data. When using the automatic loadweigh data, the link traffic counts should be the
average of the loadweigh data over the same period of time as the Oyster data. When using
the manual load counts, there is, unfortunately, only one measurement on each link, so no
averaging is possible. By far the most complex aspect of this approach is the estimation of
the pkij from the assignment process.
The primary weaknesses of this approach, compared with the other approaches reviewed,
are as follows.
77
• It treats the given link flows as deterministic constraints, which may not be ideal
for counts coming from sources with small sample sizes (i.e. manual counts) and/or
potential for significant measurement error.
• It does not explicitly account for the varying statistical quality among the inputs.
• It does not provide measures of statistical quality of the OD estimates.
Another limitation of this approach, common to all of the approaches reviewed, is that
it does not ensure that the estimated OD flows are not smaller than the corresponding OD
flows in the seed matrix. This is appropriate for the generic problem for which most of these
approaches were formulated – adjusting prior OD matrices based on measured link flows.
This application is somewhat different in that the Oyster seed matrix is considered a lower
bound on the actual OD matrix, so it is possible that this bound will be violated by the IM
estimation process. While it would be trivial to add this constraint to the formulation, such
a constraint would likely invalidate the simple and efficient solution algorithm for which this
method was selected. The addition of such a constraint should be the subject of further
research.
5.4
Exploratory Analysis of OD Estimation Inputs
This section presents some brief exploratory analyses derived from the assignment model
and the various available data sources.
5.4.1
Oyster Seed Matrix
The seed OD matrix was estimated as the daily number of Oyster journeys on each OD flow
departing during the AM Peak averaged over all 22 weekdays of March, 2009. This Oyster
seed matrix has 733,087 total passengers over 85,444 non-zero OD flows, the distribution of
which is shown in Figure 5.6(a). The smallest OD flows are 0.045 passengers (i.e. a single
observed journey over the entire 22 days) and the largest is 3,160 passengers from Waterloo
to Canary Wharf.
Of all the non-zero flows in this seed matrix, 8,742 of them have a positive probability
of using the London Overground, according to the outputs of the assignment model. This
matrix has 24,814 total passengers over these OD flows, the largest of which is 505 passengers
from Stratford to Highbury & Islington. When clamped to the Overground network, the
matrix reduces to 21,620 passengers over 1,763 flows between pairs of Overground stations.
The distribution of unclamped flows in this matrix is shown in Figure 5.6(b). According
to the assignment model, 85% of these flows and 78% of the passengers on these flows are,
respectively, guaranteed to use Overground services at some point in the journey.
5.4.2
Link Flows
The manual counts conducted over March, 2009, give a single point estimate of “service link
flows” – the number of passengers on board each individual scheduled London Overground
78
−1
0
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2
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0.8
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(a) Whole seed matrix
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0.4
0.2
0.0
Cumulative probability of flow
●
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1
2
log10(flow)
(b) Flows with positive probability of using
the London Overground
Figure 5-6: Distribution of non-zero OD flows in Oyster AM Peak seed OD matrix
service on each link between consecutive stations (e.g. the 08:06 train from Stratford to
Richmond, between Stratford and Hackney Wick). Consistent with general TfL practice,
each scheduled service is classified into a specific time period (e.g. AM Peak) depending on
the departure time of that service from its originating terminal. Aggregation of service link
flows to the AM Peak level yields the link flows with which the OD matrix will be estimated.
The distribution of aggregate counted AM Peak link flows, shown in Figure 5.7(a), ranges
from 154 passengers (Gospel Oak to Upper Holloway) to 5,886 passengers (Canonbury to
Highbury & Islington).
The assignment model, applied to the Oyster seed matrix, yields the “Oyster link flow”
of each link as per Equation (5-6). Consistent with expectations, no Oyster link flow for the
AM Peak is greater than the corresponding manual count. Figure 5.7(b) plots the counted
link flows against the Oyster link flows. The two most apparent outlier link flows in this
figure, with counted flows above 2,000 but Oyster flows below 1,000, are Clapham Junction
f lowOyster
= 0.16) and West Brompton to Kensington Olympia (0.21),
to West Brompton ( f lowcounted
the first two northbound links on the West London Line.
Table 5-2 aggregates the ratio of assigned Oyster flow to counted flow by line. Consistent
with the two outliers mentioned, the assigned Oyster flow is substantially lower on the West
London line than on other parts of the network. This is consistent with the expectation
of a low rate of fully-validated Oyster journeys on the West London Line because of large
numbers of non-Oyster interchange passengers using the West London Line at Clapham
Junction (a major National Rail interchange).
79
1.0
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flowOyster
flowcounted
(a) Counted link flows
(b) Counted link flow vs assigned Oyster link
flow
Figure 5-7: Counted and assigned Oyster link flows for AM Peak, March 2009
Line
NLL
GOB
WAT
WLL
P
f lowOyster
P
f lowcounted
0.67
0.65
0.56
0.29
Table 5-2: Aggregate ratio of assigned Oyster flow to counted flow, by line
5.4.3
Gateline Data
Unfortunately, the gateline data it not so consistent. As of March 2009, 32 stations with
London Overground services were gated, 11 of which are exclusive to the Overground. It
is hoped that for these 11 stations, gatelines could provide automatic estimates of total
passengers (i.e. Oyster and non-Oyster) entering and exiting the Overground network. This
data is validated primarily by comparing the gateline entries and exits with the daily totals
from the Oyster database, as shown in Figure 5-8.
At all these 11 stations, gateline entries are consistently greater than Oyster entries
(with a few exceptions), which is as expected. The exceptions are 17 March at Homerton, 13
March - 25 March at Dalston Kingsland, and 31 March at West Hampstead, where gateline
entrances drop off precipitously with no correlated change in Oyster data. On the other
hand, gateline exits are consistently fewer than Oyster exits at Watford High Street and
at Camden Road, where the gateline exit volumes are quite erratic. These discrepancies
between Oyster and gateline data could be the result of a range of factors, including faults
in the gatelines or station staff allowing passengers to validate their Oyster cards and then
exit without using the gates.
As discussed above, the assignment model does not explicitly record, for a given OD flow,
station entrances and exits during out-of-station interchanges (OSI’s). Similarly, the Oyster
80
AM Peak Volume
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Date (Weekdays Only)
Figure 5-8: Oyster and gateline entry and exit counts at stations exclusive to the London
Overground with recorded gateline data, March 2009 weekday AM Peak periods
data as provided indicates only the first station of entrance and last station of exit and not
intermediate validations. This may or may not be the cause of the wide gap between gateline
and Oyster entries at West Hampstead, where passengers can transfer from National Rail
and from the Underground’s Jubilee Line to the Overground’s North London Line. These
potential sources of error are set aside for now, but may be worth attention in the future,
particularly if Oyster data is reported with intermediate validations.
Despite its obvious flaws, the following selective use of these gateline data should improve
the OD estimation results. In this work, gateline data was averaged at the station level (for
the AM Peak time period) to be used in the OD estimation process, with the following
exceptions.
• Because there are two stations where all exit counts are apparently flawed, all exit
counts were disregarded.
• The exceptions mentioned above, where gateline entrances are obviously but temporarily flawed, were manually removed from the data set.
If, in the future, gateline data is judged to be of higher quality, it can perhaps be used
without such intervention.
5.5
OD Estimation Results
An AM Peak OD matrix for the London Overground was estimated from an Oyster seed
matrix, manually-counted on-board link flows, and automatic gateline entry flows, using the
Information Minimization formulation. The resultant OD matrix reproduces all given link
81
flows (on-board and gateline) to within ± 1%. To show the effects of using selected gateline
data, the OD matrix was also estimated without gateline entries.
Table 5-3 shows summary statistics for the two resulting OD estimates. The total number
of Overground AM Peak passengers (i.e. the sum of the clamped OD matrix) is slightly
smaller when estimated with gateline entry flows, but in both cases is between 37,000 and
38,000 spread over 1,763 different origin-destination combinations. This represents an overall
expansion of between 71% and 75% over the Oyster-only seed matrix of 21,620 Overground
passengers. The Total Demand Scale, the minimum and maximum possible sums of the
clamped OD matrix such that the given link flows are reproduced, is 25,202 to 150,559. This
indicates that the Oyster-based seed matrix plays a significant role in determining the total
estimated number of Overground passengers.
Source of Link Flows
Onboard Link Counts
+ Gateline Entries
Sum of Clamped Expansion Over
Estimated Matrix
Seed Matrix
37,731
74.5%
37,124
71.7%
Number of Number of
Flows > 0 Flows ≥ 1.0
1,763
1,245
1,763
1,238
Table 5-3: Summary statistics for London Overground estimated AM Peak OD matrix
Figure 5.9(a) plots OD flows estimated with gateline data, clamped to the Overground
network, against the respective flow in the Oyster-based seed matrix. Points above and to
the left of the dashed line of unit slope are flows that were expanded under the estimation
process. Table 5-4 identifies some of the largest estimated flows that expanded the most in
absolute and/or relative terms. Consistent with expectations, these are flows from Overground terminals, primarily Stratford and Clapham Junction, that are large shared facilities
with interchanges to other rail services. It is worth noting that because the origin stations
of these OD flows are terminals, the estimated number of boardings at these stations will,
by the nature of the IM estimation process, match the given values almost exactly (i.e. to
within the convergence criteria).
Origin
Strat.
Strat.
Clap. Jn.
Clap. Jn.
Clap. Jn.
Rich.
Destination
High. & Isl.
Camd. Rd.
W. Brom.
Shep. Bush
Kens. Oly.
Gunn.
Clamped OD Flow
Oyster Estimated
Expansion
505
1,073 568 (112%)
346
629 283 (82%)
78
849 771 (988%)
195
818 623 (319%)
73
592 519 (711%)
54
350 296 (548%)
Alightings at Destination
Counted Estimated
Error
3,555
3,184 -371 (-10%)
1,778
1,799 -21 (-1%)
1,115
1,560 445 (40%)
1,193
1,144
49 (4%)
1,053
1,014 -39 (-4%)
1,211
1,290
79 (7%)
Table 5-4: Selected OD flows with large estimated values and large relative and/or absolute
expansions
The expansion of the flows from Clapham Junction to points on the West London Line are
especially large in relative terms – 988% to West Brompton, 711% to Kensington Olympia,
and 319% to Shepherd’s Bush. These are the first, second, and third stops (out of four) on
the West London Line from Clapham Junction to Willesden Junction. This is a potential
82
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Figure 5-9: Estimated OD flow vs OD flow from the Oyster seed matrix, clamped to London
Overground network
cause for concern, because large relative expansions of short OD flows (i.e. those covering
only a few links) can be a reflection of inconsistencies between the assignment model, the
seed matrix, and the given link flows.
That said, these large expansions from Clapham Junction are generally consistent with
anecdotal observation on the part of the author and the expectations of Overground management (Bratton, 2010). As was shown in Table 5-2, the West London Line has a particularly
low Oyster penetration rate. Figure 5-10 plots the estimated flows against Oyster flows by
Overground line. It is clear from this plot that, as a group, flows on the West London Line
are expanded differently from flows on the other lines. Moreover, the estimated total number
of alightings at the destination stations of these flows is within 10% of the surveyed value,
with the exception of West Brompton. Comprehensive validation of this sort is discussed
further in Section 5.5.1.
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Figure 5-10: Estimated OD flow vs OD flow from the Oyster seed matrix, by London Overground Line
83
Even though the seed matrix should represent a lower bound, as discussed in Section 5.3,
it is possible for flows to shrink in this OD estimation method. Figure 5.9(b) zooms in closer
to the origin of Figure 5.9(a) for inspection of smaller OD flows. While 91% of clamped
flows expand under the estimation process, the other 9% shrink, a few quite drastically in
relative terms. The two most severe examples of this are Hatch End and Carpenders Park,
respectively, to Harrow & Wealdstone. These flows had 24 and 35 passengers, respectively,
in the clamped seed matrix but near zero passengers in the estimated matrix. The total
estimated boardings at the origin stations of these flows match the respective surveyed
values to within fewer than 10 passengers, but the total estimated alightings at Harrow &
Wealdstone is estimated at only 41% of the actual value. These OD flows, like some of the
OD flows that suffered very large relative expansions, are assigned to only two or three links.
Further investigation of the flows that were expanded or reduced beyond reasonable
expectations is merited. It is possible that these unexpected results reflect inaccuracies in
the otherwise-reasonable results of the assignment model. It is also possible that they reflect
gaps (i.e. bias) in the seed matrix, likely the result of low Oyster penetration in certain
segments of the traveling population. While it is certain that the methodology developed
here is imperfect, it may represent an improvement on the current practice at the Overground,
as explored in the following section.
5.5.1
Validation
This section presents a comparison of the new London Overground OD matrix estimate to
the OD matrix estimated by the RailPlan regional model. The on-board link loads used
here to estimate this new OD matrix came from a set of manual counts that also indicate
the number of passengers boarding and alighting each service at each station. Since these
boarding and alighting counts were not used in the OD estimation process, they can be
used to validate the OD estimation results. This is consistent with the structure of the OD
estimation problem as discussed in Section 5.2.1.
The assignment model translates the estimated OD matrix into a set of estimated boarding and alighting flows. These are aggregated to the station level, and compared against the
manual counts according to different measures of performance, each with its own advantages
and disadvantages. For two vectors (in this case sets of boarding counts) xi , vi , i ∈ 1..N ,
with xi representing the estimated or experimental results and vi representing the validation
“ground truths,” the following performance measures can be calculated.
• Percent Error (%E) – the percent error of the sum of the two sets of values, measuring
the difference in total flow.
• Percent Absolute Error (%AE) – the sum of absolute errors over the sum of the validation values, shown in Equation (5-10). This is, in essence, the absolute percent error
of each value, weighted by the respective validation values.
PN
|xi − vi |
(5-10)
%AE = i=1
PN
i=1 vi
84
The advantage of this measure is that it places more weight on larger flows. The
disadvantage is that it masks errors in smaller flows.
• Mean Absolute Percent Error (MA%E) – the unweighted average of absolute percent
errors, as shown in Equation (5-11).
M A%E =
N
X
|xi − vi |
i=1
(5-11)
vi
The advantage of this measure is that it is sensitive to relative errors on smaller flows.
The disadvantage is that for small flows, an error of very few passengers can equate to
large percentage errors.
• Root Mean Square Error (RMSE) – the euclidean distance, in N dimensions, between
the estimated and validation vectors, as shown in Equation (5-12).
v
u N
uX
(5-12)
RM SE = t (xi − vi )2
i=1
The primary advantage of this measure is that it places weight on large errors, regardless of the size of the validation value. The disadvantage is that as a quantity it is hard
to interpret in a physical sense, and thus is only useful as a relative measure.
Table 5-5 shows the comparison of the two different OD estimates with the manuallycounted boardings and alightings across all Overground stations. The total estimated boardings or alightings is in all cases fewer than the total counted boardings or alightings, but by
less than 5%. This discrepancy is made worse by the addition of the gateline entry data.
This is contrary to expectations, as additional information should improve the accuracy of
the estimate. However, all the station-level error measures do improve when gateline entry
flows are included in the estimation.
Boardings
Source of Link Flows
Onboard Link Counts
+ Gateline Entries
Estimated
38,496
37,941
Total
Counted
38,800
38,800
Alightings
Source of Link Flows
Onboard Link Counts
+ Gateline Entries
Total
Estimated Counted
38,496
39,748
37,941
39,748
By Station
MA%E RMSE
17.8%
158.7
15.7%
136.9
%E
-0.8%
-2.2%
%AE
13.4%
10.6%
%E
-3.1%
-4.5%
By Station
%AE MA%E RMSE
15.0% 19.8%
167.3
13.0% 18.2%
153.5
Table 5-5: Comparison of estimated and counted boardings and alightings
The OD matrix estimated from on-board link flows and gateline entry flows is thus
taken as the best Oyster-based OD estimate. The OD matrix currently used by Overground
planners and managers was estimated using the RailPlan regional public transport model
85
in 2008, before the opening of the new Shepherd’s Bush station. Table 5-6 presents a
comparative validation of these two matrices at the line segment,4 line, and network levels.
For the sake of this analysis, the two stations served by multiple Overground lines – Gospel
Oak and Willesden Junction – are separated into the “interchange” (INT) line. The Oysterbased estimate is validated against 2009 boarding and alighting counts (as above) while the
RailPlan estimate is validated against 2008 boarding and alighting counts.
Line
NLL
NLL
NLL
NLL
WAT
WAT
WAT
WAT
WLL
GOB
INT
(Total)
RailPlan, 2008
Oyster-based, 2009
Segment
Est. Count
%E %AE MA%E RMSE
Est. Count
%E %AE MA%E RMSE
NLLE
11,935 12,691 -6% 19% 32% 322 12,435 13,093 -5% 6%
8% 177
NLLC
3,198 4,297 -26% 54% 60% 503 4,022 3,694
9% 16% 20% 134
NLLW
2,382 2,696 -12% 30% 28% 207 3,024 2,830
7% 8% 10%
85
(Total) 17,515 19,684 -11% 28% 39% 363 19,481 19,617 -1% 8% 12% 148
WATN
1,787 1,809 -1% 44% 43% 171 1,699 1,734 -2% 4%
7%
17
WATC
3,518 4,457 -21% 34% 32% 249 3,862 4,428 -13% 13% 14% 111
WATS
962
876 10% 47% 54% 157 1,066
793 34% 34% 54% 112
(Total)
6,267 7,142 -12% 38% 39% 212 6,627 6,955 -5% 14% 18%
91
(Total)
2,784 2,876 -3% 7% 20%
93 4,079 3,580 14% 16% 43% 246
(Total)
2,977 4,035 -26% 31% 34% 135 3,664 3,985 -8% 9%
9%
44
(Total)
3,007 3,201 -6% 13% 18% 236 4,090 4,663 -12% 12% 14% 298
(Total) 32,550 36,938 -12% 27% 36% 267 37,941 38,800 -2% 11% 16% 137
Table 5-6: Line and line segment level validation on counted AM Peak boardings for RailPlan
(2008) and Oyster-based OD estimates
At Transport for London, the RailPlan model is typically validated against total boardings (i.e. %E) at the line or line segment level (Warner, 2010). By this measure, the Oysterbased OD estimate is more accurate than RailPlan for all lines but one. For the North
London Line (NLL), Watford DC Line, and Gospel Oak to Barking Line (GOB), it is more
accurate by 10, 8, and 18 percentage points, respectively. For these lines, the new OD
matrix underestimates total boardings by only 1%, 5%, and 8%, respectively, but RailPlan
understimated total boardings by much more. The West London Line is the exception here,
with boardings overestimated by 14%, as compared to RailPlan’s 3% under-estimate. For
the entire Overground network, the new OD matrix underestimates total boardings by 2%
compared to 12% for RailPlan.
For the more disaggregate station-by-station performance measurements, the Oysterbased matrix is also substantially more precise in most cases. For example, consider the
Eastern portion of the North London Line (NLLE), between Stratford and Kentish Town
West, inclusive – the busiest segment of the Overground network. The %AE and MA%E
for this segment are a third (or less) of the values for the RailPlan matrix. The same can
be observed for most other segments and lines on the network, with the primary exceptions
of the West London Line and the Southern portion of the Watford DC Line. It should
be noted that if West Brompton is excluded from the West London Line, the %AE and
MA%E improve to 3% and 10% respectively, much better than RailPlan’s results. Over the
whole Overground network, these two measures are 11% and 16% for the new OD estimate
compared with 27% and 36% for RailPlan.
4
Line segment definitions can be found in Appendix B.
86
It is clear that while the OD estimation methodology developed here is not perfect, it is
substantially better in most cases for estimating current demand levels and travel patterns
than that currently used by the Overground. This should not be surprising, since RailPlan
is estimated based only on regional household travel surveys and does not incorporate any
direct measurements of travel patterns or volumes on the network.
5.5.2
Loadweigh Sensitivity Analysis
This section uses simulation to explore the sensitivity of the OD estimation process to random
error in the measured link flows. The intent is to assess the robustness of the OD estimation
process to the measurement error associated with loadweigh data described in Chapter 4.
This data source is the only one addressed because the other inputs – the Oyster system and
automatic gatelines – are considered to have little if any random measurement error. For the
sake of this analysis, it is assumed that the link flows on which the OD matrix was estimated
are the true average link flows. That they were actually derived from manual counts rather
than loadweigh data is immaterial here.
The results of Chapter 4 are interpreted to mean that each measurement of the number of
passengers on a given train is subject to a random normally distributed additive error term
with mean zero and standard deviation of 10 passengers. In other words, the loadweigh
estimate of number of passengers L̂ is a random variable that is the sum of the true number
of passengers, L, (a non-random quantity) and an error term, , according to the following
equations.
L̂ = L + ∼ N (µ = 0, σ = 10.0)
(5-13)
(5-14)
In a certain sense, the strongest part of this assumption is that the measurement error is not
correlated with the number of passengers, which is consistent with the findings in Chapter
4 and in Nielsen et al. (2008a).
Simulations were used to test (i) the effect of this type of measurement error on the
outcome of the OD estimation process and (ii) the degree to which the availability of larger
volumes of loadweigh data can be exploited to minimize these effects. The goal of these
simulations is to test only the effects of the loadweigh measurement error and not the effects
of other sources of stochasticity such as day-to-day variation in demand. Consequently, it is
assumed here that the manual on-board passenger counts represent the true average number
of passengers on each link on each scheduled service and that this number does not change
over time. Exploiting this assumption and the properties of the normal distribution, the
simulated average of loadweigh measurements taken over d days, L̂d , can be written as
L̂d = L + d ,
10
.
d ∼ N µd = 0, σd = √
d
(5-15)
(5-16)
Two sets of thirty simulations each were run based on these assumptions. The first
set simulates the use of five days (i.e. one week) of loadweigh data to estimate on-board
87
link flows. The second set simulates the use of the average of forty days (i.e. eight weeks) of
loadweigh data to estimate on-board link flows. Each simulation run consists of the following
steps.
1. Each individual manual on-board passenger count is perturbed randomly according to
Equations (5-15) and (5-16).
2. Any counts that are randomly perturbed to be less than zero are set to zero.
3. Individual counts are aggregated, as in the previous section, to the link and time period
(i.e. AM Peak) level.
4. The OD matrix is re-estimated, using the same Oyster seed matrix and gateline entry
counts as previously.
5. The resultant OD matrix is clamped to the London Overground network and the
validation measures from Section 5.5.1 are calculated, at the level of OD flows, with
respect to the clamped OD matrix estimated on unperturbed data in the previous
section.
The error introduced into the OD estimate by the simulated loadweigh measurement
error is summarized in Table 5-7. It appears that the simulated random loadweigh error
does effect the estimated OD matrix, but that averaging over forty days of data reduces the
effect significantly. For example, the average %AE and MA%E under five days of data are
20.1% and 39.1%, respectively5 . These are unacceptable deviations, but are reduced to 1.4%
and 2.2%, respectively under forty days of data.
days
5 days
40 days
% Error
2.88%
0.02%
%AE
20.1%
1.4%
MA%E RMSE
39.1%
15.0
2.2%
0.9
Table 5-7: Average values of validation measures for OD estimation under simulated loadweigh error
Figure 5-11 plots the distribution of two of the validation measures – the total percent
error (i.e. the difference in the sum of the matrices) and the percent absolute error (%AE).
On average, the simulations do not change the total number of passengers substantially, but
the distribution of this change is much tighter for the simulations of forty days of loadweigh
data. Likewise, the %AE is both lower on average and more tightly distributed for the
forty-day simulation.
The simulations presented in this section show that the OD estimation process is in fact
sensitive to errors in the measurement of on-board link flows, but that the errors can be
reduced to acceptable tolerances by averaging over larger amounts of data. This is clearly
the strength of loadweigh data – that it is continuously available in large quantities at low
5
The calculation of MA%E excludes certain edge cases which caused huge absolute percentage errors.
These were OD flows that had very small values (i.e. < .01) in the non-perturbed estimate so any increase
(e.g. to 0.05) in the perturbed was a huge change in percentage terms.
88
5 Days
40 Days
0.02
0.03
0.04
0.05
0.00
0.05
0.10
0.15
0.20
Density
0.01
Density
0.00
5 Days
40 Days
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
0.00
●
0.01
●
●
●●
●●●● ●●
●●
●●
●●
●●
●●
●
●
●
0.02
0.03
0.04
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0.05
0.00
Percent Error
(a) Percent Error (sum of matrices)
0.05
0.10
0.15
0.20
Percent Absolute Error
(b) Percent Absolute Error (flow-by-flow)
Figure 5-11: Smoothed densities of OD validation measures under simulated loadweigh error
cost – as compared to manual counts which are taken only once per counting period at high
cost.
This section did not consider day-to-day variability in loads on trains, which must exist in
practice. Chapter 4 analyzed the load on a single scheduled service on a single link, estimating
a standard deviation of the true load of 7.7 passengers. Considering this an independent error
term would approximately double the standard deviation of error in loadweigh estimates,
requiring an approximate quadrupling of the sample size to achieve the level of accuracy
found here for the simulated 40 day sample.
This should be considered a worst case scenario. The analysis in Chapter 4, for a single
peak hour service at its peak load point, was fairly speculative. Moreover, the day-to-day
variability in loads on individual services are likely not independent of each other. If one
train has more than its average number of passengers because it is running late (and thus
has a long leading headway), the train following it is likely to have fewer than average. In
other words, the total number of passengers on a given link in the whole AM Peak period
(on which the OD matrix is estimated) can be stable even when those passengers change
their distribution between individual trains because of variability in operating conditions.
5.6
Conclusions and Recommendations
This chapter developed a methodology to estimate OD matrices for railway networks from
multiple automatic data sources, including aggregate journey data from AFC systems, automatic entry/exit counts from station gatelines, and on-board passenger loads estimated
from loadweigh data, and applied this method to the London Overground network. This
section presents first some conclusions drawn from the analysis in this chapter, and next
some recommendations based on those conclusions.
89
5.6.1
Conclusions
The following conclusions are drawn in this chapter.
• Link flows from loadweigh measurements and/or manual on-board link counts can be
combined, through a mathematical estimation process, with aggregate transactional
data from the Oyster smartcard ticketing system to estimate time period level OD
matrices for the London Overground network.
• The overall accuracy of the OD estimate is improved by the addition of automatic entry
and/or exit totals from gatelines at stations exclusive to the Overground. However,
these gateline totals must be compared with corresponding Oyster totals to identify
and remove faulty data.
• Of the wide range of available mathematical models and methods, a relatively simple
approach is sufficient to use these data sources to improve the accuracy and timeliness
of OD matrices for the Overground network compared with the existing OD matrix
from the RailPlan regional model.
• The key outputs of the network assignment model developed here, which does not
account for congestion or capacity constraints, are relatively insensitive to most embedded assumptions regarding passenger path choice. Specifically, the choice for most
passengers of whether or not to use the Overground network does not change when
most of the model’s assumptions are violated. One assumption to which the model
is sensitive is indifference between interavailable services. The assignment results do
change significantly when this feature of the model is disregarded, so it is concluded
that this is an important feature that should not be neglected.
• The Information Minimization method for OD estimation from link flows and a seed
matrix is suitable to the problem faced by the Overground. It is simple to implement,
is conceptually very similar to the matrix estimation method used by the London
Underground, and has the very important feature that its results are not sensitive to
overall scaling of the seed matrix when total number of passengers (i.e. the sum of
the OD matrix) is not fixed. This final feature is key to the Overground application
because the Oyster seed matrix is a lower bound on the true OD matrix and, unlike
in the London Underground case, the available data are such that the total number of
passengers is determined by the OD estimation process.
• The OD estimation process developed here is insensitive to measurement error in the
loadweigh data under two conditions. First, that the measurement error is unbiased
and uncorrelated with the actual number of passengers, which has been found to be
the case in this and other work. Second, that there is a sufficient quantity of loadweigh
data (i.e. at least eight weeks) over which to estimate average loads.
• There is evidence that this OD estimation process may expand some shorter OD flows
beyond reasonable limits in order to match the given link flows. This is most apparent
for certain OD flows on the West London Line, but it is impossible to conclude that
90
this behavior is in fact erroneous in most or all cases. One reasonable explanation of
this behavior is the low penetration rate of Oyster along this corridor, especially for
National Rail passengers interchanging at Clapham Junction.
• The OD estimation method developed here does not treat the seed matrix as a lower
bound of the estimated matrix, and some estimated OD flows are in fact lower than
their respective values in the seed matrix. In this sense, the method lacks a constraint
that is necessary to faithfully model the real-world phenomenon. The violation of this
constraint is not considered a serious problem for this method. It affects only a very
small portion of the OD flows, and those it does affect are for the most part relatively
small flows to begin with.
Broadly speaking, it is concluded that the methodology developed here would represent
an improvement with respect to the Overground’s current practices, but that there is also
potential for further improvement.
5.6.2
Recommendations
The methods developed in this chapter should be adopted by the London Overground, and
should be considered by other railways with similar available data. The assignment model
is custom tailored to the specific circumstances of this particular railway, and so may not
be applicable to other situations. The OD estimation method, drawn directly from existing
literature, is more likely of use in a broader range of contexts. It should be considered in other
circumstances where AFC systems provide a high quality (if not perfectly representative)
seed matrix and where link flows can be estimated with sufficient confidence that they can
be considered deterministic constraints.
One particular aspect of the OD estimation methodology used here merits further research. The constraint of the seed matrix as a lower bound on the final OD estimate should
be added to the Information Minimization formulation. It is trivial to add this constraint
to the formulation, but it may make the model much more difficult if not impossible to
solve efficiently. It is possible that a lagrangean analysis similar to that developed by VanZuylen and Willumsen (1980) would yield an efficient algorithm as it has for the existing
formulation.
Implementation for the London Overground
In terms of application to the London Overground, the methods developed in this chapter
should be applied to the network as it exists today and extended as the network expands.
The forthcoming East London Line will be served entirely by loadweigh-enabled rolling stock,
will be fully Oyster-enabled, and most of its stations will be gated. The RODS network
representation will need to be expanded to include the new East London Line.
Unfortunately, the implementation of the proposed assignment model and estimation
method is a complex undertaking. Fortunately, the capacity to execute such a project
exists within TfL, most obviously within the Strategy and Service Development group of the
London Underground. It is that group which maintains the RODS network representation,
for the purpose of estimating OD matrices for the London Underground. Collaboration of
91
London Underground and Overground analysts on such a project would also be a first step
towards the longer-term goal of estimating integrated OD matrices for the entire London
railway network (including the Underground, Overground, DLR, and National Rail) from
Oyster and other automatic data sources.
Alternatively, a third party could be contracted to operationalize the prototypes developed for this report. Ideally this would be a party experienced in transportation modeling
as well as custom software development. It is possible that this third party would be a new
TfL modeling software and data analysis group, or it could be an external contractor.
Regardless of who takes on the task of operationalizing the methods developed in this
chapter, the working prototypes should be utilized as much as is beneficial. They are developed in the free and open source programming languages Java and R, and so are readily
available for inspection, modification, or partial or complete re-use.
92
Chapter 6
Passenger Incidence Behavior
This chapter is concerned with certain behavioral elements of passenger arrival to public
transport services. Because passengers can also arrive at certain locations via public transport services, a lexical convention is established to avoid ambiguity of exposition. Passenger
incidence is defined here as the act or event of being incident to a public transport service
with intent to use that service. Passenger arrival is defined here as the act or event of arriving
at a certain location having used public transport services. When making an interchange,
a passenger can arrive at the interchange location using one service and simultaneously be
incident to the next service he or she intends to use.
This chapter is primarily concerned with the relationship between the times of passenger
incidence and published timetables. It proposes a method to study this relationship by integrating disaggregate passenger journey data from automatic fare collection (AFC) systems
with published timetables using schedule-based assignment. The purpose of this chapter is
three-fold. Firstly, to develop a method that contributes to the study of passenger incidence
behavior across a railway network with heterogeneous service patterns and frequencies using
published timetables and AFC data. Secondly, to shed light on the incidence behavior of
London Overground passengers. Lastly, to help set the stage for the following chapters which
are concerned with measuring service quality with respect to passenger expectations, some
of which are reflected in their incidence behavior.
Section 6.1 reviews literature relevant to the purposes of this chapter, include analysis
of passenger incidence behavior and methods for schedule-based assignment. Section 6.2
defines certain analytical quantities through which incidence behavior can be studied. It
proposes a method to derive those quantities from the integration of disaggregate passenger
journey data and published timetables, and describes the means by which this method was
implemented for the Overground. Section 6.3 presents results that describe the incidence
behavior of Overground passengers. Section 6.4 offers some preliminary conclusions and
recommendations.
6.1
Literature Review
This section reviews first some of the literature on passenger incidence behavior, next the
literature on certain aspects of schedule-based assignment.
93
6.1.1
Passenger Incidence Behavior
Random Incidence
One characterization of passenger incidence behavior is that of random incidence (Larson
and Odoni, 2007). The key assumption underlying the random incidence model is that
the process of passenger arrivals to the public transport service is independent from the
vehicle departure process of the service. This implies that passengers become incident to
the service at a random time, and thus the instantaneous rate of passenger arrivals to the
service is uniform over a given period of time. Let W and H be random variables representing
passenger waiting times and service headways, respectively. A classic result of transportation
science is that under the random incidence assumption1
E[W ] =
E[H]
E[H 2 ]
=
1 + cv(H)2
2 E[H]
2
(6-1)
where E[X] is the probabilistic expectation of some random variable X; cv(H) is the coefficient of variation of H, a unitless measure of the variability of H defined as
cv(H) =
σH
;
E[H]
(6-2)
and σH is the standard deviation (the square root of the variance) of H (Osuna and Newell,
1972). The second expression in Equation 6-1 is particularly useful because it expresses
the mean passenger waiting time as the sum of two components: the waiting time due to
the mean headway (i.e. the reciprocal of service frequency) and the waiting time due to the
variability of the headways (which is one measure of service reliability). When the service
is perfectly reliable with constant headways, the mean waiting time will be simply half the
headway.
The following less well-known result, first derived in the literature by Friedman (1976)
and explored further by this author and others (Frumin et al., 2010), describes the variance
of passenger waiting times under the same random incidence assumptions:
E[H 3 ]
−
Var(W ) =
3 E[H]
E[H 2 ]
2 E[H]
2
.
(6-3)
These authors have noted that the variance of waiting time is thus a function of the symmetry
of the headway distribution, which is reflected in the E[H 3 ] term.
Behavioral Incidence
It is often assumed that the random incidence assumption holds at “short” headways (Furth
and Muller, 2006). The balance of this section reviews six studies of passenger incidence
behavior which are motivated by understanding the relationships between service headway,
service reliability, passenger incidence behavior, and passenger waiting time in a more nu1
The given result also depends on the assumption that vehicle capacity is not a binding constraint – that
all passengers are able to board the first desired departing vehicle.
94
anced fashion than is embedded in this assumption. Three of these studies depend on
manually collected data, two use data from AFC systems, and one studies the issue purely
theoretically. These studies reveal much about passenger incidence behavior, but all are
found to be limited in their general applicability by the methods with which they collect
information about passengers and the services those passengers intend to use.
Jolliffe and Hutchinson (1975) studied bus passenger incidence in South London suburbs.
They observed ten bus stops each for one hour per day over eight days (for a total of 80
hours of observation), recording the times of passenger incidence and actual and scheduled
bus departures. They characterized the reliability of the service by the standard deviation
of the difference between observed and scheduled bus departure times. They limited their
stop selection to those served by only a single bus route with a single service pattern so
as to avoid ambiguity about which service a passenger was waiting for. The authors found
that the actual average passenger waiting time was 30% less than predicted by the random
incidence model. They also found that the empirical distributions of passenger incidence
times (by time of day) had peaks just before the respective average bus departure times, and
that on individual days there were spikes in the incidence rates coincident with actual bus
departures. In other words, passengers adjust their incidence behavior, both planned and in
real time, based on knowledge of the bus timetable and historical bus performance. They
hypothesized the existence of three classes of passengers:
• With proportion q, passengers whose time of incidence is causally coincident with that
of a bus’ departure (i.e. because they saw the approaching bus from their home, a shop
window, etc).
• With proportion p(1 − q), passengers who time their arrivals to minimize expected
waiting time (i.e. based on some awareness of the timetable and reliability).
• With proportion (1 − p)(1 − q), passengers who are randomly incident.
Estimating these proportions, Jolliffe and Hutchinson found that p was positively correlated with the potential reduction in waiting time (compared with arriving randomly)
resulting from knowledge of the timetable and of service reliability. Namely, that p was correlated with the headway and with the reliability of departure times. They also found p to be
higher in the peak commuting periods rather than in the off-peak, indicating more awareness
of the timetable and/or historical reliability by commuters. This study did not propose any
model by which to estimate distributions of passenger incidence times (for example under
different headways or levels of reliability).
Bowman and Turnquist (1981) build on the concept of “aware” and “unaware” passengers
(of proportions p and (1−p), respectively) described by Jolliffe and Hutchinson (1975). They
propose a utility-based model to estimate p as well as the distribution of incidence times (and
thus the mean mean waiting time) of “aware” passengers over a given headway as a function
of the headway and reliability of bus departure times. They observed seven different bus
stops in Chicago, each served by a single (different) bus route, between 6:00 and 8:00am for
5-10 days each (approximately 105 hours total observation). The bus routes had headways
of 5-20 minutes and a range of reliabilities. As in the previous study, the authors found that
actual average waiting time was substantially less than predicted by the random incidence
model.
95
0.20
0.25
σ = 0.5
0.15
σ = 1.0
0.05
0.10
σ = 2.0
0.00
Probability of passenger incidence
0.30
Estimating their model, Bowman and Turnquist found that p was not statistically significantly different from 1.0, which they explain by the fact that all observations were taken
during peak commuting times. The estimated model predicts that the longer the headway
and the more reliable the departures, the more peaked the distribution of incidence times
will be and the closer that peak will be to the next scheduled departure time (i.e. the end of
the headway). This demonstrates what they refer to as a “safety margin” that passengers
add to reduce the chance of missing their bus when the service is known to be somewhat
unreliable. Such a safety margin can also result from unreliability in passengers’ journeys to
the public transport stop or station. Life is random – if a passenger is unsure of exactly how
long it takes to walk to the station, he or she may leave a few additional minutes to be sure
to arrive at the station before the scheduled departure time.
The model of Bowman and Turnquist is illustrated in Figure 6-1 for a 10 minute headway
and different levels of reliability of departure time. They conclude from their model that,
in general, the random incidence model underestimates the waiting time benefits of improving reliability and overestimates the waiting time benefits of increasing service frequency
(i.e. lowering the headway).2 This is because, as reliability increases passengers can better
predict departure times and so can time their incidence to decrease their waiting time. Moreover, as frequency increases incidence may become more random, thus lengthening waiting
times.
0
2
4
6
8
10
Minutes since last scheduled bus arrival
σ indicates reliability of departure time. Adopted from Bowman and Turnquist (1981).
Figure 6-1: Distributions of passenger incidence for different levels of reliability of departure
time
Furth and Muller (2006) study the issue in a theoretical context and generally agree
with the above findings. They are primarily concerned with the use of data from automatic
2
This analysis does not consider other benefits of increasing service frequency, for example decreasing the
“schedule delay” experienced by passengers whose preferred departure or arrival times do not align perfectly
with the timetable (e.g. Bates et al., 2001).
96
vehicle tracking systems to assess the impacts of reliability on passenger incidence behavior
and waiting times. They propose that passengers will react to unreliability by departing
earlier than they would with reliable services. Randomly incident “unaware” passengers will
experience unreliability as a more dispersed distribution of headways and simply allocate
additional time to their trip plan to improve the chance of arriving at their destination on
time. “Aware” passengers, whose incidence is not entirely random, will react by timing
their incidence somewhat earlier than the scheduled departure time to increase their chance
of catching the desired service. The authors characterize these reactions as the costs of
unreliability.
Luethi et al. (2007) continue with the analysis of manually-collected data on actual
passenger behavior. They use the language of probability to describe the two classes of
passengers. The first is “timetable-dependent” passengers whose incidence behavior is affected by awareness (possibly gained through their own experience with the service) of the
timetable and/or service reliability (i.e. the “aware” passengers). The second is “timetableindependent” passengers whose incidence behavior is random and so does not reflect any
such awareness (whether or not they have it). The language of timetable-dependency is
adopted for the balance of this chapter to describe the randomness of passenger incidence
behavior regardless of what exactly is driving the behavior on the part of the passengers. It
is preferred because it expresses the observed probabilistic association between two variables
(i.e. incidence times and scheduled departure times) rather than some unobserved passenger
state of mind.
Luethi et al. observed passenger incidence at 28 bus, tram, and commuter rail stations
in and around Zurich, Switzerland, with headways of 2.33-30 minutes, during morning and
evening peak hours and midday off-peak hours (for a total of approximately 200 hours).
To avoid ambiguity, they limited their station selection to non-terminal non-interchange
stations served by a single route with constant headways over the period of observation. Exploratory analysis of the observed distributions of incidence times concurred with the finding
of Bowman and Turnquist (1981) that longer headways result in more peaked distributions
of passenger incidence over a given headway. The authors observed that a substantial share
of passengers appear to be timetable-dependent for headways as low as five minutes. They
also observed spikes in the distribution at the beginning of respective headways, which they
attribute to the assumption “that some passengers know very well the reliability and average delay of the public transit service and therefore arrive regularly a short time after the
scheduled departure time.”
The primary goal of this study was to estimate distributions of passenger incidence times
over a given headway which they propose to be the weighted superposition of two distributions. The incidence times of timetable-independent passengers, with weight 1 − p, are
distributed uniformly over the headway. Timetable-dependent passengers, with weight p,
are distributed according to a Johnson SB (JSB) distribution, which is similar to the Normal
distribution but skewed to the right for certain values of its parameters. The authors modify
the JSB distribution to admit an additional parameter indicating a rightward shift for those
passengers who regularly arrive shortly after the scheduled departure time. The authors
found the fit of their bespoke distribution to the observed data to be statistically significant.
This distribution is parameterized in terms of the headway, but, unlike the model of Bowman
and Turnquist (1981), it is not parameterized in terms of the reliability of the service; it is
97
a descriptive rather than predictive model. Estimations of their model yield values of p for
the different time periods of the day, which they find to be highest in the morning peak
and lowest in the off-peak, supporting the conclusion that the incidence of commuters is
more timetable-dependent. Their data collection also included brief interviews with passengers, which indicated that timetable-dependence is also correlated with experienced service
reliability.
Csikos and Currie (2007, 2008) study this phenomenon, first cross-sectionally and then
longitudinally, using data from the AFC system of the Melbourne, Australia, heavy rail
network. In their first study they use four weeks worth of data from 07:30 to 15:00, but
limit themselves to analyzing seven particular stations (out of 209), for a total of 38,000
observations over approximately 1,470 hours. The stations are, as in the other studies,
selected to avoid ambiguity regarding which scheduled service each passenger intended to
use. They also obtained high level data about the aggregate reliability (6-minute terminal
on-time performance) of the train lines serving the selected stations. Their findings generally
confirm those of the other studies – that passenger incidence is more timetable-dependent
with a more peaked distribution during peak hours, in longer headways, and for more reliable
services.
The authors found less evidence of the “safety-margin” phenomenon than in previous
studies. The suppose that this is because the previous studies focused on bus (rather than
rail) services which may be more prone to early departures. At the station on the least
reliable rail line in their study, the authors found that the distribution of passenger incidence times peaked exactly at the time of scheduled departure and had a high fraction of
passengers incident just after this time (i.e. at the beginning of the successive headway).
They hypothesize the existence of passengers with “late running awareness” who time their
incidence to account for regular late departure of trains. They point out that such a behavior pattern would result in overestimates of actual passenger waiting time when comparing
passenger incidence times to the schedule per se.
In their second study, Csikos and Currie (2008) use the same four week data set as in
their first, but this time track individual ticket holders over time to study the consistency of
behavior. They focus on the 15,000 trips made between 06:00 and 10:00 by 1,043 individual
passengers who, as morning commuters, are expected to exhibit the most consistent behavior
patterns. They characterize the passengers by the times of incidence and the “offset” times
until the next scheduled departure. They classify passengers into four distinct archetypes
exhibiting various levels of consistency in these two variables, finding roughly equal numbers
of passengers in each of the four categories. On one end the spectrum are “like clockwork” passengers who exhibit fairly consistent behavior that often minimizes their “offset”
(i.e. waiting) time with respect to the schedule. On the other end, “largely random” passengers have very little consistency with respect to “offset” time, exhibiting largely timetableindependent behavior. All classes of passengers used (according to the timetable) numerous
different scheduled services over the observation period. A small fraction of passengers (less
than 10%) with median incidence times just after scheduled departure times exhibit serial
behavior indicating “late running awareness.” The authors’ overall conclusion in this work
is one of heterogeneity in passenger behavior, even under homogeneous conditions (i.e. at
the same station at the same time of day served by the same line).
98
Discussion
Previous research has identified a rich set of passenger incidence behaviors, and related them
to certain aspects of public transport services. It has done so using manually and automatically collected data sources, and has used automatic data to investigate the consistency of
such behaviors longitudinally over time. It has been found that the randomness of passenger
incidence behavior is highly dependent on the service headway and the reliability of the
departure time of the service to which passengers are incident.
Passenger incidence behavior has been characterized primarily in terms of how random
it appears to be with respect to the timetable and to actual vehicle departure times. The
appearance of randomness (or lack thereof) has been used to indicate the degree to which
passengers have and use knowledge of the published timetable and of actual departure times.
At longer headways, passengers have more to gain by gaining and using knowledge of the
timetable; their behavior tends to be less random, peaking somewhat before the scheduled
departure time. Passengers also appear to gain and use knowledge of the actual, rather than
scheduled, departure times. When departure times are reliable, even if they are reliably late
(or early) by a particular amount, incidence behavior tends to be less random with more
passengers being incident shortly before the reliable departure time. When departure times
are inconsistent (i.e. unreliable), passengers have less to gain from choosing any particular
time of incidence, so their behavior tends to be more random.
Passenger incidence behavior has been studied primarily for the sake of understanding
how changes to a public transport service will affect passenger waiting times. It is also of
interest because it affects the relationship between the departure times of public transport
vehicles and the passenger loads on those vehicles. In the context of managing an urban
railway, it is thus important to understand passenger incidence behaviors so that management interventions (including tactical planning) will be based on realistic assumptions going
forward. As pointed out in one of the seminal investigations on the topic by Bowman
and Turnquist (1981), the effects on passenger waiting time of one particular intervention
(i.e. increasing frequency) could be overestimated compared with a different type of intervention (i.e. improving reliability), depending on what assumptions about incidence behavior
are made.
None of the research reviewed here has studied the effect on incidence behaviors of delivering timetable or real-time information to passengers via the internet or mobile devices.
This subject is becoming increasingly important as such technologies are rapidly adopted by
public transport providers and passengers world wide.
6.1.2
Schedule-Based Assignment
The authors of all of the studies reviewed in the previous section chose their data samples
such that the linking of passengers to scheduled or actual services was straightforward. In
more complex environments – for example where passengers at a given station have a choice
of services – a more sophisticated approach is needed to study passenger incidence behavior.
One aspect of the approach that will be used in this research is that of schedule-based
assignment, which was introduced in Section 5.2. This section completes the review of the
relevant aspects of this methodology. Nuzzolo and Crisalli (2004) present a good review of
99
schedule-based assignment and the various sub-models on which it depends.
Run-Based Supply Models
As mentioned in Section 5.2, schedule-based assignment depends on a run-based model of
public transport supply. Figure 6-2 illustrates the run-based supply model described by
Nuzzolo and Crisalli (2004). This model is very similar to the line-based model of supply,
but unfolded in the temporal dimension. In such a model, each individual scheduled or actual
run (or trip) of the public transport service is represented individually by its own subgraph.
In the subgraph for a given run, the nodes represent the arrival, departure, or transit of that
run at a specific location at a specific time. The links represent travel (or dwelling) on that
run between specific points in time and space. The combination of the subgraphs of all runs
is referred to as the service subgraph.
In this run-based model, demand is also modeled with temporal as well as spatial dimensions in the demand subgraph. Nodes in this subgraph represent centroids of demand
in time, according to user departure and arrival times, and space, according to the physical
network. The access/egress subgraph joins the service and demand subgraphs with boarding
and alighting links. The union of these three subgraphs is referred to as the diachronic graph
representation. One benefit of such a representation is that shortest travel time paths can
be found via standard shortest-path network algorithms such as Bellman-Ford or Dijkstra’s
(cf Bertsimas and Tsitsiklis (1997)).
This highly granular representation can cause an explosion in the number of nodes and
links in the graph representing the public transport network. This presents a problem for
some large-scale applications in which requirements for high temporal granularity necessitate
a run-based representation. Specialized algorithms and data structures have been developed
to treat these problems in practice. Tong and Wong (1999) and Florian (2004) describe
optimizations of the above graph representations and algorithms. The core idea of these optimizations is to represent the public transport network in a more concise line-based manner
and to unfold lines into runs only as needed.
Schedule-Based Path Choice and Assignment Models
Use of a run-based supply model naturally results in paths which include the temporal
dimension. However, the path choice and assignment models used for schedule-based assignment are quite similar to those described in Section 5.2 for frequency-based assignment
(excepting the hyperpath model, which does not apply here). Some proposed variations account for hypothesized differences in passenger behavior on low and high frequency services,
respectively. Others account for the stochasticity of the transport service itself. Nuzzolo
and Crisalli (2004) review these models, with many references to additional literature on the
subject. The vagaries of these models are beyond that is needed for the methodology and
application described in this chapter, so the reader is referred to the literature for further
detail.
100
From Nuzzolo et al. (2001)
Figure 6-2: Illustration of run-based supply model
6.2
Methodology
This section proposes a method for studying passenger incidence with respect to scheduled
departure times (and implied headways). It focuses on scheduled times rather than actual
times as a starting point of analysis because actual departure times are themselves often
compared to their scheduled values. The proposed method depends on the following concepts,
for a given passenger journey.
• Attractive Departure 3 – a departure scheduled from the passenger’s station of incidence
that the passenger is or would have been willing to board, however “willing” is defined.
This concept makes explicit the possibility that some scheduled departures may not be
viable alternatives for a given passenger as a function of that passenger’s destination
and of the subsequent itinerary of those departures. For example, on a line with a
3
The use of the word “attractive” is in the tradition of Spiess and Florian (1989) and Nguyen and
Pallottino (1988) in their work on hyperpaths and optimal strategies as discussed in Chapter 5. They
defined the “attractive set” of lines as the set that a passenger is willing to board at a given location.
101
trunk and branches, passengers bound for one of the branches may experience longer
headways than those traveling only on the trunk.
• Scheduled Waiting Time (SWT) – the time the passenger should have to wait according
to the schedule, given his or her time of incidence and attractive departures. This is
defined as the length of time between passenger incidence and the next attractive
departure.
• Incidence Headway – the (scheduled) headway applicable to the passenger given his or
her time of incidence and set of attractive departures. This is defined as the length of
time between the last attractive departure prior to the time of incidence and the next
such departure after the time of incidence.
The studies of passenger incidence behavior reviewed above all selected places and times
of observation so as to avoid ambiguity with respect to each passenger’s attractive departures. They trivialized the measurement of SWT and incidence headways by selecting stations served by only a single service pattern and, in some cases, with a constant headway.
While this may be sufficient for academic studies and modeling of passenger behavior, it is
clearly inadequate for understanding behavior across an entire network. In many real-world
public transport networks, the largest numbers of passengers are incident at large stations
or terminals that provide access to heterogeneous services.
In the case of the London Overground, this is most problematic on the North London
Line (NLL). Consider, for example, passengers incident to the NLL at Stratford, one of
the Overground’s busiest stations. In 2008 peak period timetables, the NLL was running
a mostly (but not perfectly) regular 15-minute (i.e. 4tph) service all day from Stratford to
the end of the NLL at Richmond. This was augmented with occasional irregular services
– a “shuttle” that ran only as far as Camden Road, and one “special” that ran on the
NLL to Willesden Junction but then on the West London Line to Clapham Junction. It is
not immediately obvious which of these services would be attractive to a given passenger at
Stratford, and thus not clear what incidence headway each passenger experiences. To address
this issue requires knowing that passenger’s eventual destination, and possibly understanding
that passenger’s travel preferences. The previous literature avoided this issue by avoiding
stations such as Stratford altogether.
The method proposed here is designed to support the study of passenger incidence behavior while accounting for the type of ambiguity described above. It does so by estimating
SWT and incidence headway automatically from the integration of published timetables with
disaggregate AFC passenger journey data via schedule-based assignment. These two quantities are necessary, but not always sufficient, to characterize passenger incidence behavior.
They describe much about the relationship between passenger incidence and the published
timetable (with implied headways), but clearly do not reflect any explicit information about
service reliability. This method is developed as a tool to aid in study of passenger incidence
behavior in general.
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6.2.1
Behavioral Assumptions
Assume that, for a given origin, destination, and time of incidence, all passengers plan
to use the single schedule-based path (i.e. set of scheduled services) through the network
that minimizes total travel time. Additionally, assume that passengers plan itineraries to
minimize the number of total boardings up (and only up) to the point where total travel
time is not increased (e.g. in the trunk-and-branch example, branch-bound passengers won’t
board a train bound for the wrong branch just to get to the end of the trunk).
These assumptions are necessarily a simplification of the true behaviors and perceptions
of passengers. The degree to which they hold is a function of the attributes of the particular
network to which they are applied and of the behavioral preferences of the passengers in
question. In any case, these assumptions are sufficient to determine, for each passenger
journey, the attractive departures prior and subsequent to the time of incidence. SWT and
incidence headway can be determined once the times of these two departures are known.
6.2.2
Algorithm
For a given passenger journey on a given public transport network, let
SW T = the scheduled waiting time for the given journey;
HI = the incidence headway for the given journey;
I = time of passenger incidence for the given journey;
LO = location of incidence of the journey in question (i.e. the origin);
LD = destination of that journey;
Dprior = time of last attractive departure prior to I;
Dnext = time of first attractive departure after I;
Hmax = the maximum normal headway (i.e. time between any two successive departures in
the same direction from the same location) on the network;
Hmin = the minimum normal headway on the network;
Path(f rom, to, time) = a function that finds the shortest weighted travel time path from
location f rom to location to with departure time strictly greater than time, with all
travel time weights equal to 1 except for a transfer or boarding penalty that is positive
but less than Hmin ;
Departure(path) = a function that returns the scheduled departure time of path path.
The Path() function encapsulates the complexity of conducting a schedule-based assignment
for a single passenger trip. Embedded in this function is some efficient algorithm for finding
shortest weighted travel time paths in a schedule-based network. The travel time weightings
103
are such as to enforce the assumption that passengers minimize the number of boardings
(without affecting total travel time).
Algorithm 6.1 can then be used to find HI and SW T for the journey in question under
the stated assumptions. This algorithm appears quite simple because most of the complexity
in the problem is encapsulated by the Path() function. It will either find the prior attractive
departure time Dprior or determine that there is no prior attractive departure in at most
Hmax
steps. It if does find Dprior , it uses that result to determine HI .
Hmin
Lines 1 through 3 accomplish the simple task of finding the next attractive departure
and thus determining the scheduled waiting time (SWT). Lines 4 through 9 search backward
in time in increments of Hmin until either a new attractive departure time d is found or the
time has been moved by more than Hmax . Hmin is the largest step possible such that the
search will never skip over a possible attractive departure. In theory, the algorithm could
use the timetable to determine the next departure time in this backward search process
rather than blindly stepping in increments of Hmin . However, the algorithm is unaware
of particular departure times since the Path() function encapsulates all knowledge of the
timetable itself. This particular algorithmic design is motivated primarily by implementation
concerns, discussed in the following section.
Algorithm 6.1 Algorithm to find scheduled waiting time and incidence headway for a given
passenger journey
1: p := Path(LO , LD , I)
2: Dnext := Departure(p)
3: SW T := Dnext − I
4: i := I
5: d := Dnext
6: while d = Dnext or Dnext − i ≤ Hmax do
7:
i := i − Hmin
8:
d := Departure(Path(LO , LD , i))
9: end while
10: if d 6= Dnext then
11:
Dprior := d
12:
HI = Dnext − Dprior
13: else
14:
Dprior := null
15:
HI := null
16: end if
This algorithm improves on the previous approaches to finding SW T and HI by considering the timetable in the context of each individual journey. The origin and destination
of each journey determine which departures will be attractive. For example, if a passenger
is traveling from one end of a public transport line to the other, no scheduled short-turn
services4 would be attractive to that passenger because they would increase the number of
boardings without improving the total travel time.
4
A short-turn is a service that, either in the timetable or as a result of real-time control actions, turns
around before reaching the usual end of the line.
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6.2.3
Implementation
Conceptually, it is simple to implement the above methodology using Oyster journey data
and published timetables. The transaction time of the Oyster entry can be taken as the
time of incidence, and the origin and destination of the journey can be used along with the
timetable to estimate which services the journey was incident to. This section describes some
of the finer points of such an implementation.
Data Considerations
The data available for analyzing passenger incidence behavior on the London Overground
network have a number of limitations that must be considered:
• Overground timetables indicate departures in minutes but not seconds;
• the Oyster system truncates seconds from timestamps in Oyster journey data (e.g. all
transactions between 08:00:00 and 08:00:59 are recorded at 08:00:00);
• for stations with entry/exit gatelines and platform validators, available Oyster data
do not indicate where exactly in a station the validation took place;
• data on distance (or typical walking times) between station entry/exit gatelines and
train platforms was not conveniently available.
As a result, the following assumptions are made in order to apply the proposed methodology.
• It is assumed that trains are scheduled to depart at the beginning of the minute indicated on the timetable (e.g. if the timetable shows a departure at 08:00, the train is
expected to depart at 08:00:00).
• It is assumed that an Oyster journeys cannot be assigned to a departure scheduled
for the same minute as their respective entry transactions (e.g. a passenger recorded
to have entered a station at 08:00 cannot be assigned to a train that is scheduled to
depart at 08:00).
• The walking time between station entry/exit gatelines and train platforms is negligible.
In other words, incidence to a station constitutes incidence to the services at that
station.
The first two assumptions are justified. Bratton (2009) indicated that the first assumption reflects the convention understood by British railways and their passengers about the
meaning of times in published timetables. Since Oyster timestamp data are truncated, most
transactions recorded on a given minute will actually have occurred over the course of (rather
than at the beginning of) that minute – after the understood departure time of any departure
at that minute in the timetable.
The final assumption is motivated primarily by the final two data limitations stated above.
That said, it is largely justified in that (i) at most gated Overground stations, access times
between gates and platforms are generally relatively short (i.e. less than one minute), and
105
(ii) at ungated stations, passengers use Oyster validators directly on platforms. That said,
for gated stations with substantial access distances this assumption may introduce a bias
into the estimations of incidence time. Specifically, passengers may appear to be incident to
particular scheduled services earlier than they actually were (i.e. have an additional “safety
margin” equal to the access time).
Open Standards and Open Source Software
The difficulty of implementing Algorithm 6.1 is in practice a function of the difficulty of
implementing the Path() function. Fortunately, a robust implementation of such a function
is available in the free/open source software library Graphserver (Graphserver, 2009). This
package was developed primarily to support web-based public transport and multi-modal
journey planner applications, which depend on exactly the same sort of Path() function as
needed in this research. Graphserver has the added advantage that it can import multiple
timetables for different days of the week or times of year and will choose between them appropriately depending on the date and time of passenger incidence. This is particularly useful
if analyzing a sample of data that covers multiple timetables, for example when studying
changes in passenger incidence on a given network over time.
Graphserver reads timetables in the widely used General Transit Feed Specification
(GTFS) (Google, 2009). This specification was defined by Google to facilitate transfer
of public transport schedules from operators to Google to power its own web-based journey planning software. It has become a de-facto standard for public distribution of public
transport timetables. Unfortunately, Overground timetables do not (yet) come in GTFS
format, so a simple (302-line) bespoke Perl (Perl.org, 2010) script was written to do the
transformation.
Another simple (272-line) Perl script was written to implement Algorithm 6.1 for one
or many individual Oyster passenger journey records (using Graphserver for the Path()
function). This approach minimized the amount of complex network models and algorithms
that needed to be implemented, instead taking advantage of an existing piece of free, fast,
robust, and well-supported software.
6.3
Passenger Incidence Behavior on the London Overground Network
This section examines passenger incidence behavior on the London Overground network
using a large sample of passenger journey data from the Oyster smartcard ticketing system.
Section 6.3.1 describes the sample of data; Sections 6.3.2 and 6.3.3 present, validate, and
analyze the results of applying the proposed methodology to the given data. Some of the
results in this section are interpreted further in the following chapter.
6.3.1
Data
The data analyzed here is a 100% sample of all Oyster journeys between all pairs of London
Overground stations for the 52 business days from 31 March, 2008 through 10 June, 2008,
106
inclusive. This chapter is concerned primarily with the behavior of Overground passengers,
and public timetables were obtained only for the Overground network. Consequently, the
data set was filtered to include only those journeys for which it can be assumed with relative
certainty that the passenger in question used only Overground services. This filtration was
accomplished using the outputs of the assignment model of Chapter 5. The resulting data set
contains nearly 1,670,000 journeys from 54 stations on 1,442 origin-destination pairs made
by over 290,000 passengers. It constitutes approximately 53,000 station-hours of observation
of passenger incidence to Overground services.
The methodology described in the previous section was applied to each Oyster journey
in the data set. This processing took some number of hours for the entire data set, but
was entirely automated. It results in a large set of observations for which the following are
measured or estimated:
• the date and time of incidence,
• the location (i.e. station) of incidence (i.e. the journey’s origin),
• the journey’s destination,
• the scheduled waiting time (SWT),
• the incidence headway,
• the Overground line to which the passenger was incident.
For Overground-only journeys that require an interchange (of which there are relatively
few), the above is measured or estimated for only the first incidence event. It should be
noted that this data set does not include journeys that interchanged to the Overground but
with initial Oyster validations elsewhere in the railway system (e.g. Underground passengers
interchanging from the London Underground’s Central or Jubilee lines to the North London
Line at Stratford). Nor does it include journeys initially incident to the Overground but
interchanging to other railway services before final validation. Journeys with interchanges
to and/or from buses will be included here, since the Oyster system effectively separates the
recording of bus and rail journeys.
6.3.2
Validation
As a point of validation, Figure 6-3 plots distributions of incidence headway for passengers
on the Gospel Oak to Barking (GOB) and North London (NLL) lines. The findings are
consistent with expectations. On the NLL, the mode of all the distributions is 15 minutes,
reflecting the core service. The distribution is more concentrated during the Inter-Peak
period, when there are no scheduled “shuttles” or “specials.” The opposite is true on the
GOB which runs a regular 20 minute service in the peak periods but transitions to and
from a 30 minute service in the Inter-Peak period. The AM Peak distribution is somewhat
more dispersed than that of the PM Peak because it includes a transition from 30 minute
headways in the early morning.
107
AM Peak
Inter−Peak
PM Peak
GOB
Relative Frequency
NLL
5
10 15 20 25 30
5
10 15 20 25 30
5
10 15 20 25 30
Incidence Headway (min)
Figure 6-3: Distributions of passenger incidence headways, by line and time period
Some values in Figure 6-3, for example 3 minutes on the NLL in the AM Peak, are
positive but observed very infrequently. This is because of slight variations in the timetable
where a pair of services that are, for example, 4 minutes apart at most stations are only 3
minutes apart at one or two stations.
6.3.3
Results
Consistent with the reviewed studies of passenger incidence behavior, the first results of
interest are distributions of passenger incidence time over a given headway. Figure 6-4 plots
these distributions for the London Overground network by line and by time period. In this
plot, incidence times are normalized by the incidence headway because different passengers
experience different incidence headways. Prior to this normalization, incidence times (from
which seconds were truncated by the Oyster system) are randomly perturbed by between 0
and 59 seconds so as to smooth the plots.
It is clear from Figure 6-4 that passenger incidence behavior, with respect to published
timetables, varies spatially and temporally across the Overground network. For example,
passenger incidence during AM Peak commuting hours is much more peaked (i.e. timetabledependent) on the GOB and Watford DC (WAT) lines, each with 20 minute headways, than
on the NLL, with 7-15 minute headways. Also, the NLL is acknowledged by Overground
management to have the most serious reliability problems (Bratton, 2008). These variations
are generally consistent with what has been found in the literature – that passenger incidence
is more timetable-dependent with a more peaked distribution during in longer headways and
for more reliable services.
Also consistent with the literature is that, for all lines, the distribution is more peaked
in the AM Peak period than in the PM Peak or midday Inter-Peak periods. It appears that
Overground commuters in the AM Peak period, likely with knowledge of the timetable and
the service, exhibit less random incidence behavior than passengers in other time periods
despite the shorter headways and less reliable service found in the AM peak.
The peaks of all of the distributions are somewhat before the very end of the headway,
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Early
AM Peak
Inter−Peak
PM Peak
Evening
Late
GOB
Relative Frequency of Passenger Incidences
NLL
WAT
WLL
0
0.25
0.5
0.75
1 0
0.25
0.5
0.75
1 0
0.25
0.5
0.75
1 0
0.25
0.5
0.75
1 0
0.25
0.5
0.75
1 0
0.25
0.5
0.75
1
Time Since Prior Attractive Departure (Normalized by Incidence Headway)
Figure 6-4: Distributions of passenger incidence, by London Overground line and time period
indicating some type of “safety margin” or waiting time-minimization behavior on the part
of passengers. Many of the distributions have small spikes at the beginning of the headway,
indicating possible “late running awareness” among some passengers. While such awareness
may in fact be found on the Overground, it is also possible that it is the passengers themselves
who are running late. They may be planning to take a train scheduled to depart at a certain
time but, because of uncontrollable circumstances or just their own poor planning, arrive at
the station shortly after that departure time.
Figure 6-5 shows the mean waiting time, for each line and time period, under two different
models of passenger behavior and train operations. First, it is assumed that all passengers
are randomly incident to constant headway services, so the mean waiting time is calculated
as half the mean incidence headway. Second, no behavioral assumption is made but all trains
are assumed to run as per the timetable, so the “Observed” mean waiting time is calculated
as simply the mean SWT. Figure 6-5 thus indicates the effects of the observed incidence
behaviors (compared with random incidence) on passenger waiting times.
On the NLL, the relatively slight skew in the incidence distributions translate into relatively small impacts on waiting time. In the AM Peak timetable dependence decreases
waiting time by 7.2% from 6.82 minutes to 6.33 minutes (about 30 seconds). In the InterPeak and PM Peak periods, the reductions are only 0.2% and 2.2%, respectively. On the
GOB, on the other hand, the implications of timetable-dependence are substantial. In the
AM Peak, the waiting time decreases by 29% from from 10.5 minutes to 7.4 minutes (3.1
minutes). In the Inter-Peak and PM Peak periods, the reductions are still 20.4% and 17.5%,
respectively.
In the model for average waiting time used in the assignment model of Section 5.3.1,
no service would be assigned a mean passenger waiting time over 10 minutes. The results
109
NLL
14
12
10
8
6
4
2
0
GOB
Incidence Behavior
Random
Observed
14
12
10
8
6
4
2
0
WAT
Mean Waiting Time (min)
14
12
10
8
6
4
2
0
WLL
14
12
10
8
6
4
2
0
Early
AM Peak
Inter−Peak
PM Peak
Evening
Late
Time Period
Red horizontal line highlights a waiting time of 10 minutes
Figure 6-5: Mean scheduled passenger waiting time by London Overground line and time
period
of this section lend support to that model. Regular weekday headways on the Overground
network go as high as 30 minutes, but the observed mean scheduled waiting time is above
11 minutes in only two cases (on the WLL during the Inter-Peak and Evening time periods)
and is never above 12.1 minutes.
6.4
Conclusions and Recommendations
This chapter developed a methodology to relate disaggregate AFC journey data to published timetables for the purpose of studying passenger incidence behavior, and applied this
methodology to the London Overground. This section presents first some conclusions drawn
from the analysis in this chapter, and next some recommendations based on those conclusions.
6.4.1
Conclusions
The following conclusions are drawn about the methodology developed in this chapter.
Firstly, that it can be used to study passenger incidence behavior using large samples of
disaggregate journey data from AFC systems such as the Oyster smartcard system. It is
able to efficiently process thousands or millions of such data records. Secondly, that it can
for each passenger journey estimate scheduled waiting time and incidence headway, two of
the most important quantities for studying passenger incidence, even under quite heteroge110
neous conditions. This estimation is dependent on certain assumptions that are believed to
be reasonable for the London Overground network, but may not be appropriate in all circumstances. Finally, that this methodology can be easily implemented using open standard
timetable formats and free software tools.
With respect to the Overground, the following can be concluded from the results in this
chapter. Broadly, that passenger incidence behavior is heterogeneous across the network and
across times of day, and that the differences are broadly reflective of what has been found
in the literature to date. Specifically, that incidence appears to be much less timetabledependent on the North London Line (NLL) than on the other Overground lines. This
chapter has not attempted to rigorously identify the causes of these differences. Hypotheses
drawn from existing literature on the subject and knowledge of the Overground network
include (i) shorter headways (i.e. higher frequencies) and (ii) less reliable service on this line
as compared to others. On the lines with timetable-dependent incidence behavior (i.e. other
than the NLL), passengers reduce their mean scheduled waiting time by over 3 minutes, or
up to 30%, during daytime hours compared with random incidence behavior. On the NLL,
such reductions are much smaller, in some cases nearly zero, in both relative and absolute
terms.
6.4.2
Recommendations
The method developed in this chapter, which builds heavily on some of the basic concepts of
schedule-based assignment, should be used to support further study of passenger incidence
behavior. The work of Bowman and Turnquist (1981) has been influential in shaping the
understanding of the relationships between headway, reliability, passenger behavior, and
waiting time. Their work should be updated using the method of this chapter to easily
analyze large samples of passenger data across heterogeneous networks. Their work also
depends on measurements of service reliability, which should be gathered from automatic
vehicle-tracking systems. The London Overground network represents an ideal opportunity
to conduct such a study – its passengers can clearly be studied via Oyster data, and its
trains are tracked by a computerized signaling system. Once the East London Line opens,
the network will have headways ranging from 5 to 30 minutes during most hours of the day.
Nearly three decades have passed since the work of Bowman and Turnquist. In that time,
many strides have been made towards informing passengers in real time about the status of
public transport services. Such information is now often distributed via in-station signs and
announcements as well as over the internet to passengers’ computers and, more importantly,
mobile devices. It is crucial to advance the understanding of passenger incidence to include
the effects of real-time information. This requires careful thinking and research designs, but
should be able to take advantage of the methodology developed here.
The methodology and results of this chapter, in particular the disaggregate application of
schedule-based assignment and the degree of timetable-independence of incidence behavior
on the North London Line, have certain service quality measurement and tactical planning
implications for the Overground. These are explored in the following chapters.
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112
Chapter 7
Service Quality Measurement from
AFC Data
The Transit1 Capacity and Quality of Service Manual defines service quality 2 as “the overall
measured or perceived performance of [public transport] service from the passenger’s point
of view” (Kittelson & Associates, Inc et al., 2003a). A related guidebook (Kittelson & Associates, Inc et al., 2003b) points out that the public transport agency or operator3 often
perceives system performance from a different perspective, one more concerned with the
quality of the operations than of the service as experienced by passengers. It defines service
delivery in terms of how well “an agency deliver[s] the service it promises on a day-to-day
basis.” In this and the following chapters, service quality will refer to the passenger’s perspective on system performance while service delivery will refer to the operator’s perspective.
As an example of the difference, consider a hypothetical “right-time” railway which, despite
running every train exactly to the timetable, happens to have insufficient capacity to serve
all of its demand at all times. The railway may consider its performance to be perfect, but
passengers riding cheek-to-jowl or on occasion left standing on the platform would likely
perceive the situation differently.
This discrepancy motivates the study of service quality itself, which is the subject of this
and the following chapter. Some aspects of service quality have traditionally been modeled
using operational data such as vehicle movement records (e.g. Wilson et al., 1992). With the
introduction of automatic fare collection (AFC) systems and the data they produce about
individual passenger journeys, it is now possible to measure certain aspects of service quality
directly. Some AFC systems (e.g. Oyster) control entry to and exit from the public transport
network. In this case, actual passenger journey time through the network can be estimated
as the difference between the timestamps of the exit and entry transactions.
Direct and automatic observation of passenger journey times creates many opportunities
for measuring service quality. One particular measure that is explored in this chapter is
excess journey time (EJT). At the level of a single journey, EJT is the difference between
actual journey time and some pre-defined journey time standard, however that standard is
1
Public transport is also known, particularly in the United States, as “transit.”
They use “quality of service.”
3
Operator here refers to the operating company or organization, not, unless otherwise stated, to the
individual vehicle driver.
2
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defined. A positive value indicates that the journey took longer than the standard allows; a
negative value indicates that it was shorter.
Section 7.1 reviews some of the literature on public transport service delivery and service
quality measurement, including EJT. Section 7.2 discusses the implications of incidence
behavior for establishing EJT standards, and proposes an analytical framework with which
to analyze EJT under different incidence behaviors. Section 7.3 uses a rigorous probabilistic
analysis to prove, under the proposed framework, that a single means for measuring aggregate
EJT appropriately can accommodate a range of incidence behaviors. Section 7.4 discusses
some important considerations for applying EJT in practice, including the interpretation of
individual and aggregate negative EJT measurements. Section 7.5 draws conclusions, and
Chapter 8 applies the method developed here to the London Overground network.
7.1
Service Delivery and Service Quality Measurement
Literature Review
The literature on measurement of public transport performance, including service delivery
and service quality, is rich. Interest in the subject has renewed since the introduction of
systems for automatically monitoring various aspects of public transport operations and,
most recently, public transport passenger journeys. This section has a dialectic quality,
which should not come as a surprise since it is about two subjects which are formulated as
perspectives of two very different entities. Section 7.1.1 and Section 7.1.2 discuss measures
of service delivery and service quality, respectively, which are found to be somewhat at odds
with each other. Section 7.1.3 discusses measures of relative service quality, which resolve
some of the tensions between pure measures of service delivery and service quality. Excess
journey time (EJT), the subject of the final sections of this chapter, is one such measure.
Before discussing the literature on specific measures of service delivery and service quality
(i.e. from the operator’s and passenger’s perspectives) this section discusses first the notion
of reliability, and next some of the goals behind conducting such measurement in the first
place.
Reliability
Reliability is a much-discussed topic in academia as well as in real world management of
public transport systems. Abkowitz et al. (1978) conducted a seminal study on reliability,
which they define as “the invariability of service attributes which influence the decisions of
travelers and transportation providers.” The definition offered by Abkowitz et al. is useful
in the context of this chapter for three reasons. First, it focuses the discussion on attributes
of public transport service outcomes, rather than inputs (e.g. mechanical components, staff)
which may have their own measures of reliability. Secondly, it defines reliability in terms of
the higher-order moments (i.e. “variability”) of these attributes of service outcomes. Lastly,
it indicates that these attributes are experienced by passengers and/or operators.
Under this definition, the discussion of reliability is quite naturally subsumed by discussions of service delivery and quality if and when they consider higher-order moments of the
attributes perceived by operators and by passengers, respectively. Consequently, much of
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what has been said about reliability applies to both service delivery and quality, and thus
applies to the balance of this chapter and indeed this thesis.
Abkowitz et al. go on to investigate public transport service reliability from a number
of different angles, including (i) how it is perceived by passengers and affects their attitudes
and behavior, (ii) how it is perceived and acted upon by operators, (iii) reasons and ways
to measure it, (iv) the factors that affect it, and (v) strategies to improve it. This study
appears to have set the stage for much of the work on the subject in the intervening decades,
some of which is described here. Uniman (2009) provides a detailed review of the work by
these and other authors on the subject of reliability.
Goals and Applications of Service Delivery and Quality Measurement
A guidebook on public transport performance measurement prepared for the US Federal
Transit Administration (Kittelson & Associates, Inc et al., 2003b) notes that public transport
providers measure their performance, broadly defined, because (i) regulation requires it, (ii)
it is useful for internal management purposes, and (iii) external stakeholders, including the
riding public and funding bodies, depend on accurate information to support advocacy and
decision-making processes. This chapter and thesis are primarily concerned with the second
of these reasons – internal management, including tactical planning. The guidebook also
describes many other stakeholders, motivations, goals, guidelines, and outcomes related to
public transport performance measurement which are beyond the scope of this thesis.
Understanding “reliability” as a proxy for overall performance, including service delivery
and service quality, Abkowitz et al. note that measuring performance from the operator’s
and passenger’s perspectives should help public transport providers to:4 “(i) identify and
understand performance problems; (ii) identify and measure actual improvements in performance; (iii) relate such improvements to particular strategies; (iv) modify strategies, methods, designs to obtain greater performance improvements.” In the context of this thesis, this
description is useful in that it establishes the measurement of service delivery and service
quality as elements of an iterative analytical management and planning process.
Cham (2006), also studying reliability, distinguishes between two primary means by which
public transport providers should be able to improve performance through the use of automatic data sources. Firstly, through improved monitoring and direct management tasks,
including evaluation of operational staff. Secondly, through improved tactical planning,
which is the focus of this thesis.
7.1.1
Service Delivery Measurement and The Operator’s Perspective
Kittelson & Associates, Inc et al. present a wide array of measures covering different aspects
of public transport system performance. Many of these measures, particularly those that are
not concerned directly with transport service outcomes, are beyond the scope of this thesis.
Those related to transport service outcomes are typically relative in that they indicate the
4
In this quotation, “performance” is substituted for “reliability,” consistent with the understanding of
reliability as one aspect of overall performance.
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degree to which service delivery adhered to the service plan. Furth et al. (2006) describe two
such classes of service delivery measures that can be developed from automatic data sources
– those measuring adherence to timetables and those measuring adherence to headways.
Timetable-Based Measures
Timetable-based measures are often based on observations of schedule deviation – the difference, for a given service, between the scheduled and actual time of arriving, passing, or
departing a given timepoint.5 The most popular measure of timetable adherence is on-time
performance (OTP), the fraction of services with schedule deviation within some threshold
(Kittelson & Associates, Inc et al., 2003b). Under the name of Public Performance Measure (PPM), this is the current measure of performance on the London Overground and all
other National Rail services in the UK, with a train considered “on time” if it is less than
5 minutes late at the destination terminal (Office of Rail Regulation, 2008). London Buses
also measures OTP, with an on-time window of 2.5 minutes early to 5 minutes late, for “low
frequency”6 routes (Camilletti, 2003).
Henderson et al. (1990) and Henderson, Adkins and Kwong (1991) offer a number of
criticisms of OTP, primarily for its lack of passenger orientation. Among these criticisms
are (i) OTP measures performance at terminals, which for many networks are remote from
the locations to which most passengers are bound, (ii) OTP typically counts as late services
which have missed part of their trip or skipped stops, even if these adjustments don’t affect
many passengers, (iii) passenger waiting times are not accurately reflected, (iv) focusing on
OTP can incentivize dispatch actions that favor schedule adherence over regular headways
and can make passengers worse off, and (v) OTP, while offering a probabilistic measure, does
not represent the odds of on-time arrival realistically.
A related measure is terminal-to-terminal running time. Statistics of the distribution of
running time indicate the reliability of a service and are important inputs into the scheduling
process. When running times are too short, some vehicles will not be in place to make
subsequent trips; when they are too long, resources are not used efficiently and terminals
may be congested (Furth et al., 2006; Furth and Muller, 2007) (see Rahbee, 1999, 2006, for
studies of the Boston and Chicago metro systems, respectively).
Another common timetable-based service delivery measure is en-route schedule adherence
(ESA), which can be defined as the fraction of services with schedule deviation within some
threshold at a given set of timepoints. This is similar to OTP, but applied at multiple points
along a line. The distribution of schedule deviation and segment (i.e. point-to-point) running
times can also be studied (Furth et al., 2006; Hammerle et al., 2005) (see Cham, 2006, for a
study of Boston bus services).
ESA (or lack thereof) is not necessarily a problem for passengers per se, since, as shown in
Chapter 6, in some cases they can adjust their incidence behavior based on their knowledge of
observed system performance. Passengers with non-random incidence behavior can adjust
their behavior to account for predictably late (or early) services, while random incidence
passengers may not notice any problem at all if headways remain even because every service
5
A timepoint is simply a location at which service arrivals, passings, or departures are timed. Timepoints
are used in scheduling as well as in performance measurement.
6
London Buses’ distinction between low and high frequency routes is discussed in Section 7.1.4.
116
is late (or early) by the same amount. It is when the degree of ESA is unpredictable (i.e. the
service is unreliable) that passengers suffer the most negative effects. However, to truly
understand those negative effects, the situation must be considered from the passenger’s
perspective.
These measures of schedule adherence treat each service in isolation, ignoring the attributes of service (waiting time) that depend on the headways between successive services
at a given location (Reddy et al., 2009). In some circumstances the headways are more important than the specific arrival and/or departure times in the timetables, thus motivating
the headway-based measures described in the following section.
Headway-Based Measures
Some public transport networks or lines publish service headways but not timetables. In some
cases, particularly for higher frequency services, it is assumed that passengers do not use the
timetable even if it is available (Kittelson & Associates, Inc et al., 2003a). As discussed in
Chapter 6, mean headway and variability of headway both affect waiting times, particularly
for randomly-incident passengers. For these reasons, headway is typically evaluated in terms
of regularity, which can be defined in a number of ways (Furth et al., 2006).
Kittelson & Associates, Inc et al. recommend measuring the mean observed headway and
the coefficient of variation with respect to the mean scheduled headway. Henderson, Kwong
and Heba (1991) proposes two measures of headway regularity, one based on Gini’s ratio
and the other based on the coefficient of variation, that have the benefit of being normalized
on a zero to one scale for comparison across services with different mean headways. These
measures are all unitless, and thus hard to interpret in physical terms relevant to operators
or passengers (Furth et al., 2006).
Reddy et al. (2009) and Hammerle et al. (2005) define headway regularity in terms of
the fraction of observed headways that are within some absolute or relative deviation from
the scheduled headway. These have the benefit of being easy to interpret by operators, but
still fail to translate easily into passenger terms (Furth et al., 2006).
The adoption of headway-based measures is motivated by the effect of headways on passenger waiting times, and so is a real step towards representing the passenger’s perspective.
Nevertheless, they are still an indirect proxy for the passenger experience, since waiting times
are related to but not equal to headways. Moreover, headway-based measures do not account
for the entire duration of passenger journeys, which are important. Finally, as discussed in
Chapter 6, headway at a given location depends on which services one is willing to board at
that location (e.g. for trunk-and-branch services), which depends on where one is headed –
headways cannot be accurately measured without considering the passenger’s perspective.
7.1.2
Service Quality Measurement and The Passenger’s Perspective
Service quality has many aspects, some easier to measure than others. Some aspects, for example those related to travel or waiting times, can be expressed in quantitative terms, while
others, such as the customer experience dealing with staff, are more clearly understood
qualitatively (Kittelson & Associates, Inc et al., 2003a). Qualitative aspects are typically
117
measured through surveys (e.g. Lu et al., 2009). The quantitative aspects of service quality
can be interpreted objectively or subjectively. Total journey time would be an objective
quantity, whereas journey time weighted to reflect passenger preferences would be a subjective one.
Strictly speaking, service quality is absolute in nature, at least with respect to service
delivery. For example, the service quality of a public transport network can be judged on its
waiting and travel times. Even when every passenger experiences perfect service delivery –
more frequent and faster service is always better. The work described in this section seeks
to measure service quality in absolute terms.
For randomly incident passengers, Osuna and Newell (1972) describe how mean waiting
times can be modeled given observations of actual headways. Friedman (1976) extends this
result to model the variance of waiting times (see Section 6.1.1 for more information on
both). Larson and Odoni (2007) describe how the complete distribution of waiting times of
randomly incident passengers can be derived from headway observations.
Bates et al. (2001) provide an in-depth investigation of how passengers value reliability
(expressed as the variability of total journey time) and how it may affect their behavior.
Furth and Muller (2006) operationalize some of this analysis by proposing to measure the
effect of reliability as additional waiting time costs perceived by passengers. Their analysis
is based in part on the literature discussed in Chapter 6 which found that passengers adjust their incidence behavior based on knowledge of schedule and headway adherence and
reliability. For short headway services (on which they assume all passengers are randomly
incident), they propose to use headway observations to measure the “potential waiting time”
as the difference between the “budgeted” 95th percentile waiting time and the mean waiting
time. This is intended to represent additional waiting time (with respect to the average case
under observed circumstances) that passengers would have to budget to assure late arrival
at their destination on at most 5% of trips (assuming en-route travel times are constant).
It represents an additional penalty that passengers pay for the unreliability of the service
headways, albeit a penalty paid in most cases by arriving early at their destination. A similar measure is developed with respect to mean and 95th percentile schedule deviation for
timetable-dependent passengers.
Chan (2007) and Wilson et al. (2008) extend the potential waiting time concept to the
entire journey. They use data from the Oyster smartcard ticketing system to measure (rather
than model) the journey times of London Underground passengers. They estimate the
distribution of end-to-end journey times for each origin-destination (OD) station pair and
find the “reliability buffer time” (RBT) 7 as the difference between the 95th and 50th (median)
percentiles. This metric is aggregated from the OD pair to the line or network level by means
of an OD flow-weighted average. It is interpreted similarly to the measure proposed by Furth
and Muller (2006) but with some advantages. Chief among those advantages are that it (i)
analyzes the entire journey, rather than just the waiting portion, and (ii) automatically and
accurately accounts for the effects of congestion, including delays suffered by passengers who
suffer additional waiting time because of trains that are too crowded to board. Indeed, these
are advantages of any approach using direct measurements of observed journey time (OJT).
7
These authors used the term “reliability factor;” Uniman (2009) later used “reliability buffer time,” a
more fitting term, which is used here.
118
Uniman (2009) notes that some “irreducible” amount of variability in passenger journey
times is to be expected because of randomness in waiting times, variation in walking speeds,
and normal but acceptable variability in service outcomes. Uniman proposes to divide observation periods into two classes of reliability levels – “recurrent” and “incident-related.”
Passengers experience normal levels of journey time variability in the former, and abnormal
levels in the latter. Also studying the London Underground, Uniman makes this classification using a statistical technique that did not consider the perspectives of the managers
of the system under study. Uniman then proposes as a measure of service quality “excess
reliability buffer time” (ERBT) – the difference in RBT for journeys from all observation
periods together and RBT for only those journeys in periods of recurrent reliability. In other
words, a measure of how far the tail of the travel time distribution is extended as a result of
abnormal operating conditions.
Uniman proposes ERBT as an attempt to create insight into the causes of unreliability by
isolating the effects of incidents. However, it is not clear that the world can be so easily and
neatly divided into recurrent or incident-related conditions. The author of this thesis spent
several months working in the control center of the New York City Subway, and observed
first hand that incidents on a continuum of severity occur constantly. It is often unclear
whether or not some perturbation to the service is normal and what in fact constitutes
an “incident.” Moreover, this measure applies cleanly only to randomly incident passengers.
Additional research is necessary to understand how to apply it to passengers whose incidence
is dependent on the timetable and/or experience with observed departure times.
The measures discussed in this section are developed entirely with reference to actual
operating conditions and passenger journeys, not with reference any service delivery commitments (i.e. the timetable, and headways and travel times implied therein). This author
has found no evidence that any of these measures are regularly used in practice by public
transport providers.
Such measures may not yet have been adopted because they do not provide information
in terms that operators can easily relate to. That said, they still have a place in the tactical
planning process, particularly when timetables are changed. In this case, measures of absolute service quality may be the only way to meaningfully capture the effects on passengers
of a particular tactical planning intervention.
7.1.3
Relative Service Quality
A compromise between measures of service delivery and measures of service quality is described in this section, which measures what is referred to here as relative service quality.
They measure service quality not in absolute terms, but rather with respect to certain standards derived from service delivery commitments (e.g. the timetable).
Wilson et al. (1992) estimate mean passenger waiting time from automatic headway
measurements in the Boston subway system using the random incidence model described in
Section 6.1.1. They estimate the mean waiting time according to the scheduled headways.
The difference between these two estimates, called “excess waiting time” (EWT), indicates
the waiting time experienced by passengers above and beyond what they would have waited
had all headways been exactly as scheduled. London Buses uses this measure to monitor
performance of high frequency routes (Camilletti, 1998). Historically, it used manual sur119
veyors to measure headways for estimating EWT at selected points in the network. With
the delivery of the new GPS-based “iBus” system, EWT will be calculated automatically
(London Buses, 2009).
London Transport (1999) extended the EWT concept to the entirety of journeys on the
London Underground, comparing mean actual and schedule values of each component of
passenger journeys. Automatic data from train control systems is used to estimate EWT,
as in Wilson et al. (1992), under random incidence model. The EWT estimate is augmented
by models for estimating the fraction of passengers, based on static demand data, who are
left behind by overcrowded trains. Automatic train movement data is also used to estimate
excess on-train time, where the scheduled on-train time between any given pair of stations
is as per the timetable. Manual sampling at 27 major stations is combined with pedestrian
flow models to estimate access, egress, and interchange (i.e. walking) time as a function of
pedestrian congestion and availability of escalators and elevators. The scheduled values for
pedestrian movements are determined from manual samples under free-flow conditions.
The sum of these components is referred to as “excess journey time” (EJT). It is estimated
in unweighted and weighted forms, where weights indicate relative passenger preferences as
described in Chapter 5. Line or network level average EJT is weighted by static estimates
of passenger flows. This approach to estimating EJT depends on a number of models to
characterize the passenger experience from a range of direct automatic operational measurements and a small number of samples of pedestrian conditions. Despite the complexity of
the system used to estimate it, EJT is perceived as easy to interpret and is used to this
day as the primary means of performance measurement and management on the London
Underground.
Chan (2007) and Wilson et al. (2008) use Oyster journey data to directly estimate (rather
than model) unweighted EJT for individual journeys on the London Underground. They
measure actual journey times directly from Oyster transactions, and derive scheduled journey
time from the values in the Underground’s existing EJT measurement system (continuing
to use the random incidence model to derive mean scheduled waiting time). As discussed in
the previous section, this approach automatically and accurately accounts for the effects of
congestion on passenger journey times. For reasons that are unclear to this author, they use
twice the scheduled waiting time as in the Underground’s system (i.e. one full headway), but
exclude all Oyster journeys with measured journey times less than the respective scheduled
value.8
Chan and Wilson et al. estimate Oyster-based EJT for single-line journeys (to avoid
ambiguity of journeys with multiple routing options through the Underground network).
They estimate mean aggregate EJT at the line level, finding that these estimates do not
correspond to the model-based estimates from the London Underground. While they do not
reach any definitive conclusions as to why this would be, there is no reason to believe that
Oyster-based estimates of actual journey time should be less accurate than those derived
from a set of complex models and a variety of operational data sources and random samples.
Consequently, there is reason to believe that, given common scheduled journey time values,
unweighted Oyster-based EJT will be more accurate than model-based estimates. In any
8
The scheduled time for the full journey is simply the sum of the scheduled values of the individual
components (i.e. walking, waiting, on-train).
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case, this work estimates service quality for individual passenger journeys relative to the
timetable based on the assumption of random passenger incidence behavior.
Buneman (1984) uses schedule-based assignment (reviewed in Chapter 6) to estimate passenger on-time performance for the BART railway network in the San Francisco Bay Area.
On that network, at that time, the AFC system recorded the origin and destination station
of each passenger journey, but only the time of exit (not of entry). The network’s train
control systems also recorded all train movements. Buneman uses these data sources to conduct, for each passenger, a schedule-based assignment in reverse with respect to actual train
movements (rather than the timetable). This results in estimates of the times that passenger
departed their respective origin stations. Then, based on some hybrid assumptions about
passenger incidence behavior (i.e. 25% timetable-dependent, the rest random) and known
vehicle departures, he estimates probabilistic times of entry into the system. Given these
times, a schedule-based assignment with respect to the timetable yields probabilistic scheduled arrival times for each passenger journey at its respective destination. The difference
between actual and scheduled arrival time, in the parlance of this section, is an estimate of
schedule-based EJT.9 Buneman does not calculate aggregate EJT, but rather compares EJT
to a 5-minute threshold window to estimate passenger OTP. It appears that this measure,
perhaps in a modified form, is still used by BART over two decades later (BART, 2010).
All of the measures of relative service quality discussed in this section were developed
with the intent of representing the passenger’s perspective. However, they all make certain assumptions about passenger incidence behavior, from which they derive the standards
against which measured or modeled service quality is compared. The next section assess the
state of practice for service quality measurement, including these assumptions, and sets the
stage for the method proposed in the following sections of this chapter.
7.1.4
Discussion
The primary client of public transport performance measurements are the managers and
planners of the transport networks themselves. Ideally, they should be motivated to improve
the service quality as experienced by their primary customers, the passengers. However,
the levers over which they have the most tangible understanding and direct control are
planning and operational service delivery. Consequently, it is proposed that measures of
public transport performance should find a balance between the passenger’s and operator’s
perspectives. They should strive for fidelity to the passenger experience, but not so far that
they are not useful or interpretable by operators.
One benefit of the service delivery measures described in Section 7.1.1 is that they are
easily interpreted, and hopefully acted upon, by transport operators who deal in schedules
and headways on a daily basis. Operators can act on these measurements to improve system
performance. However, these service delivery measures can be and have been criticized for a
lack of passenger orientation; there is no guarantee that a certain improvement in operational
service delivery will benefit passengers proportionally. It is with this recognition that the
measures of service quality presented in Section 7.1.2 have been developed. These measures
9
Had AFC transaction times at origin stations been available as they are in the Oyster system, Buneman
would likely have opted for a single forward schedule-based assignment as described in Chapter 6.
121
maximize fidelity to the actual experiences of passengers, but to such a degree that they
become difficult or impossible for operators to interpret or use.
The measures of relative service quality described in Section 7.1.3 represent a compromise between the pure operator and passenger perspectives. One of these measures, excess
journey time (EJT), has found lasting application in large urban railways such as the London
Underground and BART networks. It presents a compelling alternative to the train on-time
performance (OTP) measure currently used by the London Overground. It measures the
actual passenger experience in terms of end-to-end journey time, but reports it with respect
to certain service quality standards. In the work reviewed here, those standards are derived from the timetable. There is a definite risk to this approach – in reviewing the work
of Abkowitz et al. (1978), Uniman (2009) points out that measures using the timetable as
a standard can be misleading because “a change in the [timetable] might artificially lead
to measured improvements in performance, without any changes perceived by passengers.”
In other words, relative measures of service quality may be difficult to use for longitudinal
analysis of timetable revisions.
On the other hand a standard based purely on the passenger experience could be overly
generous to operators. As discussed by Bates et al. (2001) and in Chapter 6, passengers
often adjust their behavior to account for their knowledge of service delivery. In the worst
case, this could lead to a feedback cycle where poor service delivery results in a worsened
passenger experience which leads to a looser standard, and so on – the so-called “crumbling
edge of quality.”
It is likely that, in practice, measures of relative and of absolute service quality are both
useful in tactical planning, especially since one of the primary outcomes of tactical planning
is changes to the timetable. Relative measures should provide cross sectional understanding
relative to the existing timetable, and absolute measures should be useful for longitudinal
analysis of changes to the timetable.
Given AFC data such as that produced by the Oyster smartcard system, the average
observed journey time, a measure of absolute service quality, is straightfoward to estimate.
Still remaining is how exactly to use the timetable to derive standards, against which to
measure relative service quality, which reflect realistic passenger expectations to the maximum degree possible. This is, in part, a question of passenger incidence and of what can be
assumed about passenger’s expectations based on their incidence behavior.
Journey Time Standards and Passenger Incidence Behavior
The goal of measuring EJT is to most faithfully represent the passenger’s perspective and
experience while supporting the efforts of operators to improve service delivery and quality.
To that end, measurement of EJT has two requirements:
1. to accurately estimate actual passenger journey times,
2. to set timetable-based journey time standards that match passengers’ expectations as
closely as possible.
With the advent of AFC ticketing systems, actual journey times can now be measured
simply and directly as in Wilson et al. (2008) and Uniman (2009). One issue that remains
122
unresolved, particularly as EJT is applied to networks with lower service frequencies, is how
passenger behavior and expectations relate to the published or unpublished timetable, and
thus how the timetable should be used in setting journey time standards.
Industry manuals (e.g. Kittelson & Associates, Inc et al., 2003b; Furth et al., 2006)
typically recommend timetable-based measures for lower frequency services with a headway
greater than 10 minutes, where passenger incidence is assumed to be timetable-dependent,
and headway-based measures for higher frequency (i.e. shorter headway) services, where
passenger incidence is assumed to be random. London Buses, for example, follows this
pattern, classifying bus routes as “high frequency” at frequencies of 5 or more buses per
hour (a 12 minute or lower headway), and “low frequency” otherwise (Camilletti, 1998,
2003).
Most of the relative service quality measures discussed here, including EJT on the London Underground, use the random incidence assumption to derive waiting time standards.
The model of Buneman utilizes mixed assumptions about passenger incidence behavior to
derive waiting time standards, but he acknowledges that they are arbitrary. These various
approaches depend, explicitly or implicitly, on assumptions regarding how passengers’ knowledge of the timetable affects their arrival behavior at rail stations and their expectations of
waiting and travel time (and distributions thereof).
The stated intent of these recommendations and practices is to match journey time
standard to the concerns, experiences, and expectations of passengers. The standards against
which measured or modeled service quality is compared have been explicitly derived from
these simplifying assumptions about passenger incidence behavior. However, as discussed in
Chapter 6, passenger incidence behaviors, let alone passenger expectations, are in many cases
not so clear cut. As has been shown, it is possible to have a mix of timetable-dependent and
timetable-independent passengers using the same service at the same time. In cases when
behavior is homogeneous across some segments of passengers (e.g. those traveling between a
given pair of stations), it still possible to have varying conditions across the network or even
at a given station. Trunk-and-branch services, which provide different service frequencies
to different passengers, are a prime example. Moreover, incidence behaviors are likely to
change over time as a function of changes in relevant attributes of the service (e.g. headway
and reliability). Even where the random incidence assumption has historically been justified
by a lack of posted timetables (e.g. the London Underground), the reality may be changing
as a result of internet and mobile delivery of timetable information.
This heterogeneity of incidence behavior is an additional reason, not often mentioned,
that existing measures of service delivery and (absolute or relative) service quality often
fail to appropriately account for the passenger’s experience. It presents a particular problem in measuring EJT, where different assumptions about incidence behavior could lead to
very different journey time standards. The balance of this chapter proposes and explores a
methodology for estimating aggregate EJT that, it turns out, applies equally well under a
range of assumptions regarding passenger incidence and implied journey time standards.
123
7.2
Analytical Framework and Assumptions
For clarity of exposition, the following lexical convention is adopted. The expectation of a
given quantity refers to the expected value of that quantity in the probabilistic sense. The
standard for a given quantity refers to some individual’s supposition of what that quantity
should be. Standards can be random or deterministic.
This section establishes an analytical framework for analyzing EJT. First it defines a
set of mathematical quantities for representing different temporal quantities related to a
given passenger journey, including time of incidence, total journey time, and the journey
time standard. Next it defines values for these quantities under different passenger incidence
behaviors.
In this discussion, random variables will be shown as capitals, X, known quantities as
e The following analysis considers only
lowercase, x, and standards as capitals with tildes, X.
trips along a single line without interchanges. Judgment with respect to how much this
limits the general applicability of the results should be deferred until intuition is developed
through the analysis.
7.2.1
Journey Time Components and Standards
For a given passenger, let
I = the time that passenger is incident at his or her boarding station,
f = the standard for waiting time, also referred to as the scheduled waiting time,
W
Ve = the standard for in-vehicle travel time, also referred to as the scheduled travel time,
e = the standard arrival time at the alighting station, also referred to as the scheduled
A
arrival time,
Je = the standard for end-to-end journey time from incidence at the boarding station to
arrival time at the alighting station, also referred to as the scheduled journey time,
J = the observed or actual journey time,
X = the Excess Journey Time (EJT).
With these definitions, the following equations establish the intuitive analytical framework:
e=I +W
f + Ve
A
e−I
Je = A
(7-1)
e
X = J − J.
(7-3)
(7-2)
Equation (7-1) says that the arrival time standard is the incidence time plus some standard for waiting time plus some standard for in-vehicle time. Equation (7-2) says that the
124
journey time standard is the arrival time standard less the incidence time. Equation (73) simply formalizes the definition of EJT. Naturally, the first two equations imply that
the journey time standard is the sum of the waiting time standard and the in-vehicle time
f + Ve .
standard, i.e. Je = W
Without loss of generality, consider an origin station (“station 1”) on a rail line, a randomly selected passenger traveling from that station to a destination station (“station 2”)
on the same line, a set of trains that passenger is willing to board, including a pair of those
consecutive trains scheduled to depart from station 1 towards station 2 with the first train
scheduled to depart at time t = 0. Figure 7-1 uses a time-distance diagram to illustrate the
following additional quantities relevant to this analysis.
d = the scheduled departure time from station 1 of the next train that the passenger in
question is willing to board.
h = the scheduled headway between the prior scheduled departure and the next scheduled
departure.
a = the scheduled arrival time at station 2 of the train departing station 1 at time d.
v = the scheduled running time from station 1 to station 2 of the train departing at time d.
a0 = the actual arrival time at station 2 of the train carrying the selected passenger (whichever
train that may be).
l = the difference between the actual arrival time at station 2 of the train carrying the
selected passenger and the scheduled arrival time at station 2 of the train scheduled to
depart station 1 at d.
distance
h
v
l
Station 2
ure
r
o
pri
Station 1
0
e
tur
r
a
ep
art
dep
I
td
nex
a
d
a0
time
Figure 7-1: Example Time-Distance Graph
The following useful relationships are implied by this diagram and related definitions:
125
h=d−0=d
a=d+v
a0 = a + l
J = a0 − I.
(7-4)
(7-5)
(7-6)
(7-7)
Some aspects of this framework are worth noting. Firstly, and without loss of generality,
it is conditioned upon the given passenger being incident during the specific (but arbitrary)
headway [0, h]. Secondly, there is no requirement of correspondence between the identities
of the train scheduled to arrive station 2 at a and the train actually arriving at a0 . That is, a
specific train in the timetable is scheduled to arrive at a, but the passenger arriving at a0 may
or may not be on that specific train. Finally, neither the actual waiting nor in-vehicle time
experienced by the passenger is used within this framework. The data required to apply this
framework consists only of the timetable and measurements of incidence and arrival times
for individual passengers. This framework, illustration, and notation are designed to reflect
the issues arising in measuring EJT with AFC (e.g. Oyster smartcard) data.
7.2.2
Passenger Incidence and Behavioral Assumptions
Let fI (i), i ∈ [0, d] be the probability density function for passenger incidence times during
the headway in question. This function is assumed to be continuous, representing a smoothed
description of behavior during the given headway on an average day.
It is assumed that all passengers belong to one of two behavioral classes of individuals, each with its own method for setting journey time standards. These two classes will
be referred to here as scheduled incidence and random incidence. Mathematical terms for
these classes of passengers will be superscripted with S and R, respectively, as in fIS (i) or
X R . These two classes of passengers correspond to the two broad categories of passengers
identified in studies of passenger incidence as discussed in Chapter 6.
The following sections describe the appropriate journey time standards to use for each
class of passengers. They also describe a type of probability density function for incidence
times that would be observed in the presence of each class. It will be shown later that it
is not necessary to assume that the entire set of passengers at a given station, or even on a
given origin-destination (OD) pair, come from only one of these two classes.
Scheduled Incidence
Scheduled incidence passengers are passengers whose incidence is timetable-dependent – their
behavior cannot be considered entirely random with respect to scheduled departure times.
They are assumed to have knowledge of scheduled departure times and scheduled running
times, which they use both to time their incidence and to set waiting and in-vehicle time
standards.10 It is assumed that their standard for waiting time is exactly the time between
10
This approach neglects the possibility of passengers who set their standards based on their experience
of actual train departure and running times. Such standards would result in a measure of absolute service
126
incidence and the next scheduled departure (i.e. the time they would expect to wait, given
their time of incidence, if they expected the next train to depart as per the timetable), and
that their standard for in-vehicle time is as per the timetable. In the context of the analytical
framework, this implies
fS = d − I
W
Ve S = v
(7-8)
(7-9)
which, along with Equations (7-1), (7-2), and (7-5), imply:
eS = I + (d − I) + v = a
A
JeS = a − I.
(7-10)
(7-11)
These results correspond with the simple intuition that if a passenger has knowledge
of the timetable, her standards for a given journey depend on her time of incidence only
insofar as it determines the next scheduled departure. Her standard for arrival depends only
on the timetable for that departure. These equations, along with Equations (7-6) - (7-7),
substituted into Equation (7-3) yield the similarly intuitive result that
X S = l.
(7-12)
Consequently, conditioned upon the passenger being incident on the given headway and
arriving at time a0 , EJT is independent of I and thus is not a random quantity.
Because this class of passengers are assumed to be aware of the schedule, all that is
assumed regarding the distribution of their incidence times over a given headway h is that it
is not uniform (i.e. completely random). Specifically speaking, a continuous function fIS (i)
is taken to be a probability density function for the incidence times of scheduled incidence
passengers if it meets the following conditions:
fIS (i) ≥ 0, i ∈ [0, h]
1
∃ i ∈ [0, h] : f S (i) 6=
h
Z h
fIS (i)di = 1.
(7-13)
(7-14)
(7-15)
0
Figure 7-2 shows an example of such a distribution, where the rate of passenger incidence
increases linearly as the departure time approaches, though the conditions as stated are much
less restrictive than this specific example. As discussed in Chapter 6, if such a distribution
were observed in practice, one could argue that it would then be reasonable to assume that
passengers somehow schedule their incidence, and thus it would be reasonable to use the
journey time standards in this section.
quality similar to RBT and thus contrary to the nature of EJT as a measure of service quality explicitly
relative to the timetable.
127
fIS (i)
0
h
i
Figure 7-2: Example probability density function of incidence time for scheduled incidence
passengers
Random Incidence
Random incidence passengers are passengers whose incidence behavior is completely independent of scheduled departure times. They are assumed to have knowledge of scheduled
running times and headways but not to have or not use any knowledge of scheduled train
departure times. These passengers are assumed to set standards for waiting time based on
knowledge of scheduled train headways and to set standards for in-vehicle time based on
knowledge of scheduled train running times. Specifically, it is assumed that their standard
for waiting time is exactly half the scheduled headway in which they are incident, and that
their standard for in-vehicle time is as per the timetable. In the context of the analytical
framework, this implies11
fR = h
W
2
R
e
V =v
(7-16)
(7-17)
which, along with Equations (7-1), (7-2), and (7-5), imply
eR = I + h + v
A
2
h
JeR = + v.
2
(7-18)
(7-19)
These results correspond with the intuition that if a passenger has no knowledge of
specific departure times, his standard for arrival time will depend on his time of incidence,
but that his a priori standard for total journey time is independent of his time of incidence.
These equations, substituted into Equation (7-3) and with help from Equations (7-4) - (7-7),
11
Equation (7-16) does not include the effect on waiting time of variability of scheduled headways, as
shown in Equation (6-1), because the analysis is conditioned on the passenger being incident on a specific
headway; this is the same conditioning used by Osuna and Newell (1972) to arrive at Equation (7-16).
128
yield
XR = l +
h
− I.
2
(7-20)
EJT for random incidence passengers is, unlike for scheduled incidence passengers, a
random variable, even when conditioned upon being incident in the given headway and
arriving at time a0 . This result is also intuitive, indicating that the EJT for a given randomly
incident passenger depends on luck with respect to how close his time of incidence is to
subsequent departures. This is further discussed in the following section.
For random incidence passengers, conditional upon being incident at a given station during a given scheduled headway, their specific times of incidence are assumed to be uniformly
random. In precise terms, for a passenger incident during a given headway h, the classical
assumption (e.g. Osuna and Newell, 1972) is made that
(
1
, i ∈ [0, h]
(7-21)
fIR (i) = h
0 , otherwise
which is shown in Figure 7-3. As discussed in Chapter 6, if such a distribution were observed
in practice, one could argue that it would then be reasonable to assume that passengers are
randomly incident, and thus it would reasonable to use the journey time standards in this
section.
fIR (i)
1
h
0
h
i
Figure 7-3: Example probability density function of incidence time for random incidence
passengers
7.2.3
Framework Intuitions
Under this framework, it should be intuitively clear that for a given individual passenger
journey, the wrong assumption about incidence behavior and journey time standards would
result in a biased estimation of EJT. For example, consider a passenger who is incident just
before the scheduled departure time (i.e. I = d − , h) on a day in which all trains run
perfectly to schedule and capacity is not binding (i.e. a0 = a so l = 0). Under the above
framework, if it is assumed that this was in fact a randomly (and luckily) incident passenger,
it would be estimated that X R = − h2 + . On the other hand, if it is assumed this was
129
a scheduled incidence passenger, it would be estimated that X S = 0. In this sense, it is
clear that at the level of an individual journey, correct behavioral assumptions are crucially
important to unbiased estimation of EJT. It should be noted that the bias introduced by
the wrong incidence assumption is at most one half headway.
The following sections prove analytically that, contrary to the intuition developed here,
the assumption that all passengers are scheduled incidence passengers yields an unbiased
estimator of EJT regardless of the actual passenger incidence behavior. To help see why
this would be, consider the set of all passengers incident in the same headway of the lucky
passenger in the above example. If they all were random incidence passengers, there would
also be, probabilistically speaking, an unlucky passenger who just missed the prior train
(i.e. incident at I = ). For this new passenger, under the random incidence assumption, it
would be estimated that X R = h2 − . Averaged with the EJT for the lucky passenger, this
would yield an aggregate EJT of 0, the same value as would be estimated for both of these
passengers under the assumption of scheduled incidence.
7.3
A Unified Unbiased Estimator for Aggregate Excess Journey Time
Figure 7-1 and Equations (7-4) - (7-7) describe the journey of a single passenger who is
incident on the headway [0, h] and arrives at his or her destination at time a0 . The end of the
previous section constructed a trivial example in which the wrong assumption regarding the
class of this passenger biased the estimation of EJT for this single journey. In practice there
is no intent to report EJT (i.e. estimate X) at the level of an individual passenger. Rather,
EJT should be aggregated over many passengers to indicate the performance of all or part of
the network in question over a period of time. Of interest is an estimate of the probabilistic
expectation (i.e. the mean) of X, E[X] for all passengers incident on the headway [0, h].
This section first extends the analytical framework to include multiple passengers with
multiple arrival times. It then shows that the estimator for aggregate EJT under the scheduled incidence assumptions is also an unbiased estimator for aggregate EJT under the random
incidence assumptions if passengers are in fact randomly incident. Finally, it shows that the
same estimator is unbiased under a blend of random and scheduled incidence behavior.
7.3.1
Framework for Aggregate EJT
If EJT is to be aggregated over multiple journeys, the analytical framework is insufficient
as currently constructed. Different passengers traveling between the same two stations and
incident on the same scheduled headway can have different arrival times depending on the
actual departure times of trains from the origin station. For example, if, on a given day,
trains departed station 1 at times 0, h3 , and h, and some passengers were incident on [0, h3 ]
and others were incident on [ h3 , h], then it is highly unlikely that all passengers incident on
[0, h] could have the same arrival time a0 .
To account for this, the framework is generalized. Rather than a single train arriving
at station 2 at time a0 , instead consider K discrete trains arriving at station 2. For the k th
train, k ∈ 1..K, let
130
a0k = the arrival time at station 2 of train k,
lk = the difference between the arrival time of train k and a,
Yk = an indicator random variable, for each passenger, which is 1 if the passenger arrived
on train k, 0 otherwise,
αk = the fraction of all passengers incident at station 1 on [0, h] who arrived at station 2 at
a0k , trivially equal to E[Yk ],
gIk (i) be a probability density function, defined over [0, h], describing the distribution of the
incidence time of the passengers who were incident on [0, h] and traveled from station
1 to station 2 aboard train k.
It is appropriate to model the arrival times of passengers discretely since train arrivals
are a discrete phenomena, at least as compared to passenger incidence. The set of K trains
is exhaustive in that it includes all trains used by passengers incident on [0, h] and traveling
from station 1 to station 2. This is sufficient to write that
K
X
αk = 1
(7-22)
αk gIk (i) = fI (i).
(7-23)
k=1
K
X
k=1
It will also be useful to use the law of total expectation to decompose E[X] as a function
of the respective probabilities and conditional expectations of X for passengers arriving on
each of the K trains as
K
X
E[X] =
αk E[X|Yk = 1].
(7-24)
k=1
7.3.2
Equivalence of Random and Scheduled Incidence Assumptions for Aggregate EJT of Random Incidence Passengers
In Equation (7-12) of Section (7.2.2) it was shown that under the assumption of scheduled
incidence, for a given journey incident at station 1 on [0, h] and arriving at station 2 at time
a0 , EJT is not a random variable but rather equal to l, independent of time of incidence
I. Because the extended framework uses the indicator random variable Yk , X S is a random
variable. However, conditional upon a given passenger being on train k, EJT for that
passenger is no longer random and is known to be lk , which implies that
E[X S |Yk = 1] = lk .
131
(7-25)
Substituting this into Equation (7-24) yields, quite intuitively, that under the assumption of
scheduled incidence the estimator for aggregate EJT is
E[X S ] =
K
X
αk lk .
(7-26)
k=1
Under the random incidence assumption, it was seen in Equation (7-20) that EJT for a
given journey does depend on time of incidence. However, conditioned on a specific incidence
time I = i, X R is a deterministic quantity. In the notation of the extended framework, the
law of total expectation then can be used to write that
Z h
Z h
h
R
k
R
k
gIk (i)(lk + − i) di.
(7-27)
E[X |Yk = 1] =
gI (i) E[X |I = i, Y = 1] di =
2
0
0
Substituting this result into Equation (7-24), interchanging sums with integrals, and rearranging terms, it is found that the estimator for aggregate EJT under random incidence
assumptions is
R
Z
E[X ] =
0
h
X
Z h
K
K
X
h
k
αk lk
gIk (i) di.
αk gI (i) di +
−i
2
0
k=1
k=1
(7-28)
If it is assumed that the passengers in question are in fact randomly incident, Equations
(7-21) and (7-23) can be used to write that
K
1 X
=
αk gIk (i), i ∈ [0, h].
h k=1
(7-29)
This along with the fact that the integral of any probability density function over its entire
domain equals unity simplifies Equation (7-28) to
R
Z
E[X ] =
0
h
1
h
K
X
h
− i di +
αk lk
2
k=1
(7-30)
which simplifies further to
R
E[X ] =
K
X
αk lk
(7-31)
k=1
which is the same result as found for scheduled incidence in Equation (7-26).
The estimator for aggregate EJT under scheduled incidence assumptions is thus shown to
be equal to the estimator for aggregate EJT under random incidence assumptions if passengers are in fact randomly incident. This implies that using the scheduled incidence estimator
for aggregate EJT is appropriate if all passengers are scheduled incidence passengers or all
passengers are random incidence passengers. The next section extends this result to the case
when passengers come from both classes.
This analysis was based on a conditioning of the waiting time standard for random
132
incidence passengers on the headway in which each passenger was incident. Passengers
typically arriving in a period of time that spans multiple headways could face some variability
in scheduled headways, and thus could set their standards based on the results of Equation
(6-1). The derivation of Equation (6-1) depends on the realization that, under random
incidence, more passengers will be incident in longer headways and thus have longer average
waiting times. It is intuitively felt that the analysis presented here accounts for the same
phenomena – when random incidence passengers are treated with the scheduled incidence
assumptions, more of them will be incident in longer headways and thus have longer scheduled
waiting times (with respect to the timetable) and longer journey time standards.
7.3.3
Blended Passenger Incidence Behavior
In practice, as found in Chapter 6, it will often be the case that some passengers are randomly
incident while others clearly make use of the timetable. This would be indicated by a
distribution of passenger incidence times over a given headway that is clearly a superposition
of two different incidence distributions, one meeting the scheduled incidence conditions of
Equations (7-13) - (7-15) (e.g. Figure 7-2), and one meeting the random incidence conditions
of Equation (7-21) (i.e. Figure 7-3).
This can be described as blended passenger incidence behavior, and is consistent with the
formulations for mixed incidence behavior discussed in Chapter 6. This section derives an
estimator for aggregate EJT under such blended behavior and shows that this too is equal to
the estimator under scheduled incidence assumptions. Functions and variables for blended
behavior are superscripted with B, as in JeB .
Without loss of generality, assume that some fraction γ of passengers incident on [0, h]
are random incidence passengers, and so 1 − γ are scheduled incidence passengers.12 The
probability density function for incidence times of all passengers under blended incidence
can then be written as the superposition of the respective random and scheduled incidence
density functions
fIB (i) = γfIR (i) + (1 − γ)fIS (i) , i ∈ [0, h].
(7-32)
Figure 7-4 shows an example of such a function, where fIR (i) is as shown in Figure 7-3 and
fIS (i) is as shown in Figure 7-2.
Moreover, assume that for a given passenger it is not known which behavioral class they
belong to. Let Z be an indicator random variable that is equal to 1 if a given passenger is
a random incidence passenger and 0 otherwise, and λ(i) be the probability that Z = 1 for a
passenger having been incident at time I = i. As illustrated in Figure 7-4 it can be written
formally that
γf R (i)
.
(7-33)
λ(i) = Pr(Z = 1|I = i) = BI
fI (i)
Because the behavioral class of a given passenger is no longer assumed, the journey time
standard JeB is now a random variable, equal to JeR or JeS if the passenger is a random or
scheduled incidence passenger, respectively. This can be used to define the random variable
12
γ, the proportion of random incidence passengers, is the complement to the proportion of timetabledependent passenger, p, discussed in Chapter 6.
133
fIB (i)
(1 − γ)fIS (i)
γ h1
γfIR (i)
0
i
h
i
Figure 7-4: Example probability density function of incidence time for blended random and
scheduled incidence passengers
for EJT of a single blended incidence passenger journey as
(
X R, Z = 1
XB =
.
XS, Z = 0
(7-34)
Thrice applying the law of total expectation, first on Y , next on I, and finally on Z, the
estimator for aggregate EJT under blended passenger incidence behavior can be derived by
writing
E[X B ] =
=
=
K
X
k=1
K
X
k=1
K
X
k=1
αk E[X B |Yk = 1]
Z
(7-35)
h
gIk (i) E[X B |Yk = 1, I = i] di
αk
(7-36)
0
Z
αk
h
gIk (i) λ(i) E[X R |Yk = 1, I = i] + (1 − λ(i)) E[X S |Yk = 1, I = i] di.
0
(7-37)
Fully conditioned on Y and I, the notation defined here and results of the previous section
can be used to write
Z h
K
X
h
B
k
E[X ] =
αk
gI (i) λ(i) lk + − i + (1 − λ(i))lk di
(7-38)
2
0
k=1
which is easily re-arranged to
B
E[X ] =
K
X
k=1
Z
αk
0
h
gIk (i)λ(i)
Z h
K
X
h
− i di +
αk lk
gIk (i)di.
2
0
k=1
(7-39)
Interchanging sums with integrals and rearranging the first term and simplifying the second
134
term yields
Z
h
λ(i)
0
X
K
K
X
h
k
−i
αk gI (i)di +
αk lk .
2
k=1
k=1
(7-40)
Substituting Equations (7-23) and (7-33), this result becomes
B
Z
E[X ] =
0
h
γfIR (i)
fIB (i)
K
X
h
B
− i fI (i)di +
αk lk .
2
k=1
(7-41)
Canceling terms and substituting Equation (7-21), this becomes
B
Z
E[X ] =
0
h
1
h
K
X
h
− i di +
αk lk
2
k=1
(7-42)
which is the same as Equation (7-30), again simplifying to
E[X B ] =
K
X
αk lk .
(7-43)
k=1
The estimator for aggregate EJT in the case of multiple trains carrying blended incidence
passengers is thus found to be the same as the estimator for aggregate EJT under scheduled
incidence assumptions.
7.3.4
Extension to a Heterogeneous Rail Network with Interchanges
The author’s intuition is that this analysis extends readily beyond a single rail line with a
single service pattern to a rail network with interchanges and a variety of service patterns.
Such an extension would require the model to account for passenger incidence behavior at
interchange locations. Without formally extending the model, the following observations
should provide an intuitive sense of why the schedule-based estimator for aggregate EJT is
appropriate in a network context. Note that in all cases it is expected to measure only the
end-to-end journey time, which subsumes all interchanges.
• This analysis easily extends to include a network with walking links, such as those
between AFC gatelines and station platforms. Such links can be thought of as lines
or services with continuously available departure times (i.e. infinite frequency, or zero
headway), in which case the distinction between scheduled and random incidence is
irrelevant.
• On a single line with heterogeneous service patterns, such as short turns or a trunkand-branch configuration, passengers can be considered, as in Chapter 6 to ignore
certain departures that do not improve their overall travel time. This simply changes
the timetable applicable to each passenger’s journey, not the analysis thereof.
• If passengers are aware of and make plans based on the timetable for the entire network,
then clearly the schedule-based estimator is appropriate.
135
• If passengers are unaware of or do not use the timetable for any portion of the network, and if the different services are timetabled independently, then incidence at the
interchange location will be random with respect to the departures of the service being interchanged to. In this case, some passengers will be lucky and experience short
interchange times while others will experience long ones, and the same probabilistic
smoothing seen in Section 7.3.2 should apply.
• If the timetable is designed to facilitate interchanges (i.e. minimize interchange times)
between lines, then a schedule-based estimator should be used regardless of passenger
incidence behavior and standards. Even if passengers are randomly incident at the
initial station, their incidence at the interchange station is non-random with respect
to the timetable of the subsequent line by the very nature of the specially-constructed
timetable.
• If passengers are aware of and use the timetable for only a portion of the network,
then they either interchange from a service on which they schedule their incidence to
a service on which they are randomly incident, or vice versa. In the former case, since
they do not know (or care) about the timetable for the second service, their incidence
time (and thus journey time standard) for the first service is unaffected.
• The reverse scenario, where passengers are unaware of the timetable on their first
service, but have a target departure in mind for the second, is perhaps less straightforward. In this case, it would be reasonable to set a waiting time standard of a full
(rather than half) headway for the first service, since this is what an operator would
recommend, based on the timetable, to minimize the probability of missing the second,
scheduled, departure. A first intuition is that this would bias some of the analyses in
this chapter. However, as was found in those analyses, the first intuition with respect
to incidence behavior, the timetable, and journey time standards is not always correct.
This issue merits further examination.
If these intuitions are to be believed, and the issue in the final observation is resolved, the
model and estimators for aggregate EJT developed in this chapter are in fact quite general
and should be applicable to a wide variety of contexts.
7.4
Discussion
This section anticipates and discusses some concerns that may arise in the application of the
method proposed in this chapter.
7.4.1
Application Considerations
AFC penetration rates may vary across the network for which EJT is measured. In some
cases, this may require a weighting of EJT values to account for this variation. For example,
if the rate varies significantly across different OD flows on the same line, re-weighting may be
needed when analyzing EJT on that line. If penetration is largely consistent for a given line
136
but varies across line, such correction is only necessary if comparing EJT results between
those lines. In any case, an OD estimate of the type developed in Chapter 5 should be
sufficient to re-weight values across a given network.
Care must be taken if EJT is to be measured for only some portion (e.g. the Overground)
of a broader network (e.g. the entire London railway network), especially if timetables are
available only for that portion of the network. The most straightforward way to handle
this situation is to select only those OD flows that will use the portion of the network in
question with relative certainty. This can be done manually based on judgment, or can take
advantage of an assignment model that considers the entire network such as that used in
Chapter 5.
7.4.2
Negative EJT
As mentioned, EJT for an individual passenger journey (under the scheduled incidence assumptions) can be negative. This is in and of itself not a cause for concern in terms of
the measurement of EJT. However, aggregate EJT that is net negative may indicate certain
biases in the EJT estimation process. Negative EJT for individual journeys can occur for
several reasons, including the following.
• A passenger uses some service not included in the set of timetables used in setting
journey time standards. In this case, the negative EJT can be smaller or larger in
magnitude than the headway of the service in question.
• A passenger takes the service on which he or she is scheduled to depart, but that
service arrives at that passenger’s destination earlier than the timetable indicates. In
this case, when the headway is relatively large, the negative EJT should be small in
magnitude relative to the headway of the service in question.
• A passenger takes an earlier service than the one which he or she is scheduled to
depart (because that earlier service was running late), which naturally arrives at the
passenger’s destination before the passenger’s scheduled arrival time. In this case, the
negative EJT can be as large as the headway of the service in question.
The first of these reasons indicates a potential bias the estimation of EJT. If nonscheduled trips were inserted into the timetable by the operator in question as a result
of service control decisions, the negative EJT is unbiased in that passengers would not be
considered to have expected to use this new service. However, if the service that the passenger used was provided by a different operator (e.g. one who shares the same track, or on
a different path altogether), the result can be considered a biased EJT in that the service
should have been used in setting journey time standards. This reflects a problem with the
selection of OD flows for which EJT is measured for a given operator, which may result from
biases in an assignment model used to select those OD flows.
The second and third of these reasons do affect the EJT estimate for an individual journey.
These negative EJT measurements clearly affect the distribution of EJT, but should not
under most circumstances unduly affect the mean. To better understand this phenomena,
and its relationship to passenger incidence times, consider the following example. A passenger
137
is incident to a 20 minute headway service at 08:01, one minute after a scheduled departure
time of 08:00, and the train scheduled to make that 08:00 departure runs exactly one minute
late for its entire trip. The passenger in question will have an EJT of -19 minutes (early),
but the other passengers who caught this train and were scheduled to catch this train will
have an EJT of 1 minute (late).
In this example, the one large negative EJT will be balanced out by many small positive
EJTs. Where this balance (i.e. the mean EJT) falls in general depends on the passenger
incidence behavior and on the other trains making up the service. If passengers are uniformly
and randomly incident and all trains are equally and uniformly late (i.e. maintaining an even
headway), the balance will be exact (i.e. mean EJT will be zero). This is as expected, in
that even headways are all that is required to serve random incidence passengers perfectly.
For passengers whose incidence is timetable-dependent and for trains with varying adherence to the timetable, the situation is more complex. This complexity has not been
completely analyzed, but it is felt intuitively, especially in light of the analysis of Section
7.3, that mean EJT will appropriately reflect the balance between winners (with negative
EJT) and losers (with positive EJT).
An exception to this intuition is the case when a large proportion of passengers do indeed
exhibit “late running awareness” as described in Chapter 6. When passengers are incident
after a scheduled departure time based on an expectation that trains regularly depart late,
and their expectations are correct, they will, individually, have a negative EJT close in
magnitude to the headway. If enough passengers exhibit this behavior, EJT can be net
negative, even if those passengers arrive at their destinations on time or late compared to
the schedule for the train they may have expected to take. This does not constitute a bias
in EJT measurement as defined here, but would confound the interpretation of EJT results.
Such a situation highlights the need to study passenger incidence behavior, as in Chapter 6,
before analyzing EJT.
This is an example of the potential peril of applying a measure of relative service quality
with standards based on the timetable rather than true passenger expectations. As mentioned, all of these complexities do affect the distribution of EJT, somewhat confounding the
interpretation of higher order statistics (e.g. percentiles) of EJT. These higher order statistics have important implications for measuring reliability from the passenger’s perspective.
They are not analyzed here, but are deserving of attention in future research on the subject.
7.4.3
EJT and Longitudinal Analysis
In practice, many tactical planning changes include revisions to the timetable. As discussed
in Section 7.1.4, this presents a problem for using EJT in longitudinal analyses. When the
timetable is revised, changes in EJT may be driven more by the timetable modification than
by any real changes in journey times experienced by passengers. For example, if running
times in the timetable are lengthened but passenger journey times remain the same, EJT
will decrease.
Furthermore, as discussed in Chapter 6, passengers may adjust their incidence behavior
over time as service conditions change. The method proposed here is entirely conditioned
on actual incidence behavior, so changes in such behavior will not bias estimates of EJT per
se. In one sense, this is a positive feature of this method because it absolves the analyst of
138
the need to make any assumptions regarding incidence behavior. However, it also implies
that EJT will not capture some of the benefits of improved service reliability. Specifically,
it will not reflect the benefits captured by passengers who take advantage of more reliable
service by adjusting their incidence behavior to reduce waiting time (likewise for the harm to
passengers who react to less reliable service by becoming more randomly incident incidence).
For example, consider a service that has become more reliable over time, perhaps because
of improved infrastructure or rolling stock but with no changes to the timetable. If, as a result
of this reliability improvement, passengers of this service now arrive at their destinations
closer to their respective arrival time standards, such will be reflected in EJT measurements.
However, it may also be the case that the journey time standards of some of these passengers
has decreased because, as the service has become more reliable, their incidence behavior has
become less random (i.e. more timetable-dependent, with smaller scheduled waiting times).
This would not be reflected in EJT measurements.
These realizations highlight the relative nature of EJT, and suggests that other measures,
for example those for absolute service quality, may be necessary for longitudinal analysis. It
should also be noted that measures of service quality, including EJT, are not intended to
be used for evaluating a timetable on its own merits. They simply speak to the differences
between passengers actual journeys and the promise implied by the timetable. Evaluation
of a timetable in isolation from passenger journeys is not considered here.
7.5
Conclusions
Excess journey time (EJT), with standards derived from the timetable, is a measure of
relative service quality that strikes useful balance between the passenger’s and operator’s
perspectives. It has found lasting application at a number of large urban railways. Actual
passenger journey times can now be measured (rather than modeled) directly from automatic
data produced by AFC systems such as the Oyster smartcard.
Along with measuring actual passenger journey times, EJT depends on a standard against
which to compare those measurements. These standards should be based on the timetable,
so as to be as meaningful and useful to operators as possible. Within that constraint,
they should reflect passenger concerns as realistically as possible. Most measures of service
quality and relative service quality have made the assumption of random incidence, with the
implied standard for waiting time of half the scheduled headway. As discussed in Chapter
6 passenger incidence behavior is often, including on the London Overground, much more
heterogeneous than that. This heterogeneity of behavior comes with certain implications
about what knowledge passengers have of the timetable and how they use that knowledge.
This chapter has established a rigorous framework for analyzing EJT, in particular for
reasoning about passenger’s journey time standards as implied by varying incidence behaviors. It was found that the wrong assumption about incidence behavior and journey time
standards can result in a biased estimate of EJT at the level of an individual passenger
journey. It was also shown that the estimator for aggregate EJT is unbiased, regardless of
actual passenger behavior, under the assumption that all passenger incidence and associated
journey time standards are dependent on actual departure times in the timetable. This result was proven for a single rail line without interchanges, but intuitively should hold for a
139
rail network.
This is a very useful result in practice. It allows for the estimation of aggregate EJT
from only AFC (e.g. Oyster smartcard) data and published timetables in a simple unified
manner, regardless of service frequencies or passenger behavior that vary across the network
or over time. The following chapter applies this result to the London Overground.
140
Chapter 8
Oyster-Based Excess Journey Time
on the London Overground
This chapter presents excess journey time (EJT) results for the London Overground network.
It adopts the conceptual approach proposed in Chapter 7 and implements it using published
Overground timetables and journey data from the Oyster smartcard ticketing system. It
uses some of the results observed on the Overground as consideration points for discussing
the properties and merits of EJT as a measure of service quality.
Section 8.1 describes the methodology by which EJT was measured for the Overground
network, including implementation details. Section 8.2 validates the results through graphical analysis. Section 8.3 presents EJT results for the Overground network, and compares
these results with the network’s existing measure of service delivery. Section 8.4 draws some
conclusions about the issues that arise in applying EJT to a real-world network such as
the Overground. The following chapter uses these and other EJT results to document and
evaluate a recent tactical planning exercise on the Overground network.
8.1
Excess Journey Time Methodology for the London
Overground
EJT for London Overground journeys is estimated according to the unified methodology
described in Sections 7.2 and 7.3 of the previous chapter. This method assumes that the incidence behavior and journey time standards of all passengers are dependent on the timetable.
This was shown in Section 7.3 to be unbiased in aggregate, even if some or all passengers
are in fact randomly incident.
Under the framework of Section 7.2, for each given journey recorded by the Oyster
smartcard ticketing system
• the incidence time, I, is estimated as the timestamp of the entry transaction;
• the actual arrival time, a0 , is estimated as the timestamp of the exit transaction;
• the scheduled arrival time, a, is estimated from the timetable;
141
• the total journey time, J, is estimated as a0 − I (the difference between the entry and
exit transaction times);
• the excess journey time, X, is estimated as a0 − a (the difference between the actual
and scheduled arrival times).
Figure 8-1 illustrates this method for a passenger traveling from Stratford to Camden
Road on the North London Line. In this “time-distance” plot, the X axis represents time and
the Y axis represents the distance traveled along the North London Line (NLL) in number of
stations. Each line traveling northeast through the plot shows the schedule of one weekday
service.
~
Scheduled Arrival Time (A = a): 8:29
Touch out (a'):
Camden Rd, 8:36
Distance
Excess Journey Time (X) = 7 min
Observed Journey Time (J) = 35 min
~
Scheduled Journey Time (J) = 28 min
~
Scheduled Travel Time (V) = 23 min
~
Scheduled Waiting Time (W) = 5 min
Touch in (I): Stratford, 8:01
Scheduled Departure (d): 8:06
Time
Figure 8-1: Time-distance illustration of EJT estimation for a passenger from Stratford to
Camden Road
The estimation of the scheduled arrival time, a, for each passenger is achieved through
the same schedule-based assignment process used to analyze passenger incidence behavior
in Chapter 6. The schedule-based path returned by the Path() function of Algorithm 6.1
includes information about the scheduled time of arrival at the destination station. This
assignment incorporates the following assumptions:
• No time is required to move between the points of Oyster validation (e.g. station gatelines) and train platforms.
• Trains are scheduled to depart at the beginning of the minute indicated in the timetable
(i.e. 08:00 means 08:00:00 not 08:00:59).
142
• Entry and exit transactions are uniformly distributed over the minute indicated by
the Oyster database (e.g. transactions recorded at 08:00:00 actually occur randomly
between 08:00:00 and 08:00:59).
These assumptions and their implications for the schedule-based assignment process have
already been discussed at length in Chapter 6. The first assumption is broadly justified by the
actual characteristics of most Overground stations but is adopted for convenience purposes
and could bias EJT estimates for those journeys incident at large stations very shortly before
a scheduled departure. The final assumption does not, probabilistically speaking, bias the
estimate of total journey time because entry and exit transactions both undergo the same
timestamp truncation process.
The same software and data are used here as in Chapter 6. A combination of open
source tools and scripts were used to process over 1.6 million Oyster journey records made
by over 290 thousand passengers on the 52 weekdays from 31 March, 2008 through 10 June,
2008, inclusive. As in Chapter 6, the data set was filtered to include only those journeys for
which it is almost certain (based on the assignment model of Chapter 5) that the passenger
in question used only Overground services. In that sense, EJT is estimated through a twostage assignment process. First, a frequency-based assignment is used to select journeys that
are (almost) certain to have used the Overground. Second, a schedule-based assignment is
used to determine EJT with respect to the Overground timetable for those journeys.
EJT results were not re-scaled to account for varying Oyster penetration rates across
the Overground network. This could have been accomplished using the OD estimate from
Chapter 5, but only for the AM Peak results (since only an AM Peak OD matrix was
estimated).
8.2
Graphical Validation
This section validates that aggregate Oyster-based EJT measurements accurately reflect
events on the ground, including train operations (i.e. service delivery) and the passenger’s
experience (i.e. service quality). Because of the complex and dynamic nature of even a single
day’s rail operations and passenger journeys, a graphical approach is used. An example of
the type of plot used is shown in Figure 8-2.
This plot is similar to that shown in Figure 8-1 with the addition of the times, locations,
and EJT of actual passenger journeys.1 The size of the slanted hatch marks represent the
number of Oyster journeys (in the Stratford → Richmond direction) that exited a given
station on a given minute of the day on Thursday 3 April, 2008. The color of each hatch
mark indicates the average EJT for the trips it represents. The more yellow and then red
the mark, the more positive (i.e. late) the EJT; the greener the mark, the more negative
(i.e. early) the EJT.
Unfortunately, automatic data on actual train movements was not available for this
research (though it does exist for the Overground network). However, the trails of Oyster
exits clearly describe the movement of trains over the course of a given trip along the line.
1
For station abbreviations see Appendix A
143
In this sense, the plot contains all the information needed to asses whether EJT faithfully
captures the delays incurred by passengers of degraded train service.
There is much that can be inferred from this plot about the service delivery and quality
on the day in question, for example:
• Trains arriving Richmond (RMD) after 08:00 were less patronized and ran to schedule
or a bit early.
• Starting with the 07:07 service from Stratford there are slight delays, which become
severe (i.e., bright red) for the 08:06 and 08:22, and, perhaps, also the 08:30 and 08:37
trips.
• The 08:52, 09:03, 09:22, and 09:38 services ran smoothly, at least as far as Willesden
Junction (WIJ).
• The 09:31 shuttle to Camden Road (CMD) may not have run at all, as reflected by
the late (i.e., red) passengers as far as Camden Road on the 09:38 service.
• The 09:52 from Stratford ran extremely late or not at all.
• By the 11:07 departure from Stratford, the service had largely recovered.
The above hypotheses can be judged against the true record of events found in the
Overground’s incident logs, which indicate the following:
• No NLL trains departing Stratford before 07:00 on Thursday 3 April, 2008 were more
than a minute late arriving at their destinations.
• The trains departing Stratford between 07:00 and 08:00 arrived at their destinations
between -2 minutes early and 9 minutes late.
• The 08:06 and 08:22 trains from Stratford arrived at Richmond 18 and 10 minutes late,
respectively, because of severe door problems on the 08:06 train.
• The 08:52, 09:03, 09:22, and 09:38 services were 2 minutes early and 5, 2, and 0 minutes
late, respectively, at their destinations.
• The 09:31 shuttle was cancelled, because the rolling stock scheduled for this trip was instead used for the 09:38 service, whose assigned rolling stock had been delayed inbound
from Richmond by a sick passenger.
• The 09:52 departure from Stratford was short-turned at Hackney Wick (HKW) on its
incoming trip, a knock-on effect of the above sick passenger, and arrived 11 minutes
late at Richmond.
• All trains departing Stratford between 11:00 and 12:00 were between 2 minutes early
and 3 minutes late at their destinations.
144
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Hatch marks indicate by size the number of exits (per minute) and by color the average EJT (red is positive/late, green is negative/early)
RMD
KWG
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SAT
ACC
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KNR
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EJT (min):
Figure 8-2: Time-distance plot of timetable and observed Oyster exits for westbound travel on the North London Line on 3
April, 2008
Distance
The consistency between the service inferences derived from the coupling of the Oyster
data and the timetable on the one hand and the incident logs on the other is evident.
Particularly compelling about this example is the cancellation of the 09:31 train and the
short-turn of the 09:52 train. The precise effect of these control actions on passengers,
relative to the scheduled service, is captured in the EJT measure, as shown in Figure 8-2
Validation of this sort was performed for each of the 10 weekday mornings from 31 March
2008 to 11 April 2008, inclusive, with similar results. In each case, a similar correspondence
was found between the chart and the Overground’s incident logs.
8.3
Results
This section presents EJT results for the London Overground network, first in isolation and
next in comparison to the existing measure of service delivery. The results in this section are
presented as much for the sake of exploring EJT as a measure of the passenger experience
as they are for analyzing the performance of the Overground network itself.
8.3.1
Excess Journey Time on the London Overground
Distributions and Negative EJT
Figure 8-3 plots the cumulative distributions of EJT in the AM Peak period for the NLL and
the Gospel Oak to Barking Line (GOB).2 It is not a surprise that in both cases a substantial
fraction (18% and 28%, respectively) of EJT measurements are negative, implying that
many passengers arrived at their destination earlier than the timetable indicates they should
have. The mass of the distributions, especially on the GOB, between approximately -3 and
0 minutes is likely the result of trains running slightly ahead of schedule. The distributions
effectively start at -15 minutes on the NLL and -20 minutes on the GOB, as predicted in the
discussion of negative EJT in Chapter 7 – these are the headways of those services during
the AM Peak.
Based on these results and the results in Chapter 6, it is not felt that aggregate EJT will
be meaningfully biased by the combination of “late running awareness” behavior among a
large proportion of Overground passengers coinciding with actual late running by trains.
2
These plots smooth over the Oyster timestamp truncation by adding a random perturbation uniform
on [0, 1] to each EJT measurement (not included in the calculation of the mean EJT).
146
1.00
0.75
0.75
●
0.50
Cumulative Probability of EJT
Cumulative Probability of EJT
1.00
Mean EJT: 2.6
0.25
0.00
0.50
●
Mean EJT: 1.0
0.25
0.00
−20
−10
0
10
20
30
−20
EJT (min)
−10
0
10
20
30
EJT (min)
(a) North London Line
(b) Gospel Oak to Barking Line
Figure 8-3: Distributions of EJT in AM Peak periods
Mean and Total EJT by Line and Time Period
Figures 8-4 and 8-5 show two different aggregations of EJT by line3 and time period. The
first of these presents the daily average of the sum of EJT for all Oyster journeys. This plot
emphasizes the passenger-weighted nature of EJT as a measure of system performance. It is
clear that, as a product of the number of passengers and the length of delays experienced by
those passengers, the NLL, particularly during the AM and PM Peak periods, is the most
problematic part of the Overground network. It is the line most deserving of management
and tactical planning attention; the other lines frankly pale in comparison.4 For the GOB,
the West London Line (WLL) and for interchange passengers (INT) the AM and PM Peak
periods have the most total passenger delay. The Watford DC Line (WAT) breaks this
pattern, with negative total and mean EJT in the Early and AM Peak periods. This net
negative EJT is further discussed later in this section.
Figure 8-5 shows the pure mean passenger EJT. It puts all lines and time periods on
equal footing by normalizing by the total number of journeys. This plot is primarily useful
for comparing the performance of different lines at different times of day from the perspective
of the average passenger, rather than all passengers. Overall mean EJT clearly varies across
lines and time periods. After normalizing for the total number of journeys, the AM and PM
Peak periods, with EJT of 2.6 and 2.2 minutes, respectively, are still the most problematic
periods for the NLL.
3
Lines, as in Table 2-2, represent single-line passengers. INT refers to passenger journeys interchanging
between Overground lines.
4
The numbers in Figure 8-4 are not adjusted to account for varying rates of Oyster penetration, which
should bias the relative differences in total EJT between lines. For example, Chapter 5 found in Table 5-2
that Oyster penetration in the AM Peak on the WLL was in rough terms half that of the other three lines.
However, even correcting this plot for these differences (i.e. doubling the height of the bars in the WLL
graph) would not affect the conclusion that the NLL is the source of the lion’s share of EJT.
147
GOB
WAT
WLL
INT
15000
10000
5000
E
AM arl
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te ak
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Daily Mean Total EJT (min)
NLL
Time Period
Figure 8-4: Total EJT, by line and time period
NLL
GOB
WAT
WLL
INT
3
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Mean EJT (min)
2
Time Period
Figure 8-5: Mean EJT, by line and time period
These measurements are higher than all other lines for corresponding time periods except
for interchange passengers (INT) in the AM Peak, with an EJT of 3.1 minutes. It is not
unexpected that interchange passengers (most of whom likely use the NLL for one leg of
their journey) suffer longer delays than single-line passengers. A short delay on the first
leg of an interchange journey can cause the passenger to miss the targeted departure of the
second leg. This could magnify the small delay on the first leg to an entire headway of the
service on the second leg.
The WLL is very close to the NLL in terms of mean EJT, whereas it was dwarfed in
terms of total EJT. The implication is that journeys on the WLL are subject to delays of
similar (average) magnitudes, but many fewer journeys are affected. Unlike on the NLL, the
normalization by total passengers does change the relative picture for the GOB. While total
EJT is greatest in the AM and PM Peak periods, the highest average EJT is experienced
by passengers during the Early morning period. These relative differences do not necessarily
mean that one time period or line is more worthy of attention than the other. Rather,
it presents a more nuanced picture of service quality which can be acted upon differently
depending on management policies and priorities.
EJT is net negative on the WAT in the Early and AM Peak periods. To understand this
further, EJT of WAT passengers was investigated at the level of individual origin-destination
(OD) flows. In the AM Peak, 46 out of 236 OD flows on the WAT had net negative EJT,
148
including all 15 OD flows into Euston, the line’s southern central London terminus. These
flows into Euston account for 93% of net negative EJT on the 46 net negative OD flows.
Almost half of that net negative EJT into Euston comes from the flows originating at Queens
Park and Kensal Green (towards the southern end of the line), both with average EJT
of almost -3.0 minutes. This is explained, in consultation with Overground management
(Bratton, 2010) by the fact that WAT trains often depart Queens Park on time or slightly
late and arrive Euston terminal up to 5 minutes early. In other words, their scheduled
running time over the last portion of the line is generous.
Another quarter of the net negative EJT into Euston comes from the OD flows originating
between Watford Junction and Harrow & Wealdstone (at the northern end of the line), noninclusive, which have a mean EJT of -5.1 to -12.4 minutes. This likely represents a problem
with the assignment model used to filter non-Overground passengers. Another National Rail
service provides twice-hourly express service from Watford Junction and Harrow & Wealdstone to Euston in substantially less time than the Overground. The assignment model
correctly assigns passengers from these two stations to that service, but not for passengers
who start on the Overground and interchange to this express service, perhaps opportunistically, at Harrow & Wealdstone. Further discussion of these two sources of net negative
EJT, and their implications for EJT as a tool for service quality measurement and tactical
planning, are postponed until later in this chapter.
In general, these aggregate results are in line with a priori expectations held by the
management of the Overground network (e.g. Bratton, 2008). The most strongly held belief,
confirmed here, is that the NLL carries the largest passenger loads and has the most delays,
especially during the peak periods.
Time Series of Mean EJT
Figure 8-6 shows daily mean EJT over time for each London Overground line, for the whole
day and for the AM Peak period. On all lines, there is marked day-to-day and week-to-week
variability of EJT. As expected, mean EJT exhibits some volatility on a day-to-day basis.
This is particularly the case as sample sizes decrease, namely in the AM Peak compared to
the whole day, and for the WLL and INT compared to the other lines. There is not a clear
up or down trend over time in this dataset suggesting that overall relative service quality on
the Overground was steady over this period.
149
NLL
GOB
WAT
WLL
INT
Whole Day
0
5
AM Peak
Mean EJT (min)
5
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06/08
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Figure 8-6: Daily Mean EJT
Mean and Total EJT by Time Period and Direction (NLL)
Daily Mean Total EJT (min)
Figures 8-7 and 8-8 further disaggregate EJT results for the NLL by direction of travel. This
aggregation is important because of the unbalanced nature of passenger demand on the NLL
(and indeed on many railways) in different periods of the day. Figure 8-7 shows total EJT to
be substantially worse in the westbound direction than in the eastbound direction in the AM
Peak period. Figure 8-8 shows mean EJT to be similarly unbalanced, though somewhat less
so than total EJT, in the same period. This indicates that, in the AM Peak period, there
are more passengers suffering longer delays in the westbound than the eastbound direction.
Similar results can be seen in the PM Peak period with the directions reversed, though the
unbalance is not nearly as severe as in the AM Peak.
AM Peak
Inter−Peak
PM Peak
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10,000
8,000
6,000
4,000
2,000
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West
East
West
East
West
East
Direction
Figure 8-7: Total EJT on the NLL, by time period and direction
150
Mean EJT (min)
AM Peak
Inter−Peak
PM Peak
3.0
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2.0
1.5
1.0
0.5
0.0
West
East
West
East
West
East
Direction
Figure 8-8: Mean EJT on the NLL, by time period and direction
Mean and Total EJT by Scheduled Service (NLL AM Peak)
One advantage of the approach proposed here is that, with such a large and detailed data
set, it is possible to probe deeper into the specifics of delays and their effects on passengers.
To estimate EJT, each passenger journey was assigned to a specific scheduled service. This
assignment indicates only which train a given journey would likely have taken under righttime service delivery, not which train the passenger actually rode. In that sense, each
scheduled service defines a specific market over time and space, and the assignment places
journeys into these markets.
Figures 8-9 and 8-10 aggregate EJT to the level of these markets. They show total and
mean EJT, respectively, for westbound passenger journeys on the NLL between Stratford and
Willesden Junction.5 These are the peak London Overground markets – the peak direction
(from Stratford towards Richmond) at the peak time of day on the busiest line – which were
shown in Figures 8-4 and 8-5 to have the most severe EJT problems on the whole Overground
network. The bars in these plots are spaced according to the actual headway (at Stratford)
of each service.
Figure 8-9 clearly shows that the 07:52 and 08:22 trains are the most problematic services in terms of total passenger delay. It also shows how unbalanced the headways in the
timetable are, especially between Stratford (SRA) and Camden Road (CMD).6 Between
07:00 and 09:00, the services to Richmond with full 15 minute headways have the highest
total EJT relative to their shorter-headway leaders and/or followers. This observation, along
with the finding in Chapter 6 that passengers on the NLL display incidence behavior that
is largely random, suggests a causal relationship. Because of (mostly) uniform passenger
arrival rates, the respective markets of services with longer leading headways will contain
relatively more passenger journeys. Unbalanced market sizes can translate into unbalanced
passenger loadings and overcrowding on some trains, with potentially serious implications.
Overcrowded trains can extend train dwell (and thus running) times at stations and also
impact passengers’ ability to board their desired trains. This dynamic, and its implications
for tactical planning, is further explored in the following chapter.
5
Journeys bound for west of Willesden Junction are excluded because, while most NLL services go to
Richmond, one per hour in the AM Peak divert at Willesden towards Clapham Junction.
6
These unbalanced scheduled headways are also visible in the time-distance plots in Figures 8-1 and 8-2.
151
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Daily Mean Total EJT (min)
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Figure 8-9: Total EJT by scheduled service, westbound
5
4
Mean EJT (min)
3
2
1
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Time of Departure
Figure 8-10: Mean EJT by scheduled service, westbound
The mean EJT results in Figure 8-10, normalized by the total number of journeys in
each market, show similar results. The most substantial relative differences are for the short
headway services at 07:12 and 09:07. Their mean EJT is much higher compared to other
services than was their total EJT. This stands to reason, in that with short headways they
should have fewer journeys and thus less total EJT.
8.3.2
Comparison with Existing Performance Metrics
This section compares EJT measures with corresponding on-time performance (OTP) results
from the existing London Overground performance regime, the Public Performance Measure
(PPM). These comparisons are presented as much to explore the differences between EJT
and OTP as public transport performance measures as to characterize performance on the
152
Overground.
Figure 8-11 plots PPM and total and mean EJT by line,7 for the AM Peak and for the
whole day, over the entire study period. The plot shows the complement of PPM so that
the measures are directionally aligned (i.e. a higher number indicates worse performance).
PPM and total EJT correspond in that the NLL is by far the worst performing line. The
difference between the NLL and other lines is even more pronounced in terms of total EJT
than in terms of PPM. This reflects the difference in passenger volumes between the different
Overground lines.
The WLL appears much worse than the other lines in terms of mean EJT than it is in
terms of PPM. This could be because the WLL has the lowest frequency of the Overground
lines. Consequently, each delayed train (counting against PPM) may have a greater proportionate effect on the line’s passengers. It could also be that the manner in which WLL trains
are delayed has worse effects on passengers than on the other lines.
15%
0%
20000
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30000
20000
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1.0
10000
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Line
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0.0
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0.5
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5%
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Weekday
Weekday
10%
30000
Mean EJT (min)
1 − PPM
0%
2.5
AM Peak
5%
40000
AM Peak
AM Peak
10%
Daily Mean Total EJT (min)
15%
0.0
NLL
GOB
WLL
Line
(b) Total EJT
NLL
GOB
WLL
Line
(c) Mean EJT
Figure 8-11: EJT and PPM, by line
Figure 8-12 plots mean EJT against (the complement of) PPM for the North London
Line, for the whole day and for the AM Peak, for the 52 weekdays in the study data set. As
expected, the measures are substantially but not perfectly correlated. Clearly the OTP of
NLL trains will affect the EJT of their passengers, but it is expected that EJT will capture
additional information about passenger journeys that OTP does not. In both the whole day
and the AM Peak cases there is clear variation of EJT around the linear regression fit with
PPM (adjusted R2 of .84 and .69, respectively), indicating that there is additional information captured in EJT measurements. The variation is greater in the more disaggregate AM
Peak calculations, and tends to increase as PPM decreases. This pattern suggests that PPM
reflects the passenger experience less effectively as conditions worsen.
7
The WAT is excluded here because of the problems with the assignment model discussed in the previous
section.
153
7
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Weekday
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0%
10%
20%
30%
40%
1 − PPM
Lines are simple linear regression fits. Adjusted R2 for Weekday and AM Peak are 0.84 and 0.69,
respectively
Figure 8-12: Mean EJT vs PPM, for NLL
8.4
Conclusions
This chapter presented an analysis of aggregate and disaggregate EJT results for the London Overground, both in isolation and in comparison to the Overground’s existing measure
of service delivery. This section presents some conclusions drawn from this analysis, first
regarding EJT as a measure of service quality in general, and second regarding EJT on the
Overground network itself.
As a Measure of Relative Service Quality
EJT for individual passenger journeys can be estimated through the combination of journey
data from AFC systems with published timetables by means of schedule-based assignment.
This method takes into account the scheduled and actual service delivery on the network
over the time and space of each passenger journey. The requisite schedule-based assignment
can be achieved efficiently through the use of free software tools and timetables in open
standard formats.
EJT for individual passenger journeys on a given service was found to range from negative (i.e. early) by up to one headway to positive (i.e. late) by substantially more than one
headway. A negative EJT for a single journey does not in and of itself represent a problem
or inconsistency in the measurement scheme. However, it is difficult to interpret EJT for
individual journeys, in part because of the ambiguity with respect to passenger’s standards
and incidence behavior discussed in Chapter 7. Consequently, EJT is not a particularly
useful measure to analyze individual passenger journeys.
Aggregate EJT, on the other hand, is a measure of relative service quality with clear
meaning. It expresses the average passenger’s experience in terms of total journey time com154
pared to what the timetable would imply, for a wide range of passenger incidence behaviors.
Individual EJT measurements are, by nature of the assignment process by which they are
estimated, easily aggregated both spatially and temporally. Depending on the analytical
need, aggregate EJT can be estimated at the level of line, origin-destination flow, scheduled
service, time period (e.g. AM Peak), day, week, etc.
When aggregated, EJT is by its very nature passenger-weighted. Different aggregation
functions (e.g. mean or sum) can be used to present different types of passenger orientation.
Total EJT accounts for relative volumes of passengers between different aggregation variables
(e.g. lines, times of day, etc). It can be used to assess where and when management and
planning attention could make the most overall progress towards aligning service delivery
and service quality for all passengers. Mean EJT on the other hand normalizes by number
of passengers. It can be used to assess relative service quality for the average passenger for
each aggregation variable. Neither total nor mean EJT is a better analysis tool per se; they
simply represent different analytical goals and priorities. Both aggregations capture certain
information about the passenger’s experience that a service delivery measure such as on-time
performance (OTP) does not.
Aggregate EJT was observed here to be net negative as a result of two of the three causes
discussed in Chapter 7. Firstly, trains can regularly run ahead of schedule. In this case,
aggregate EJT indicates that there is extra running time in the timetable. This illustrates a
difference between EJT and OTP – in the case of EJT, less is not always more. A negative
EJT can be as valuable an indicator as a positive EJT that tactical planning attention is
required. OTP, on the other hand, can never go beyond 100%, and so will not explicitly
indicate excessive running time in the timetable.
Secondly, aggregate EJT can be net negative because of problems with the assignment
models used to estimate EJT for individual journeys. Incorrect modeling assumptions or
missing timetables, for example, can result in passengers being able to reach their destinations by a different (and substantially faster) route than the assignment process implies.
This is an error, or bias, in the estimation process. It highlights the sensitivity of EJT to
certain behavioral aspects of the assignment model.
No evidence was found of the final cause of net negative EJT – an outsized proportion
of passengers being incident shortly after a scheduled departure time to catch a train that
they expect to, and that does, depart late. Such could still occur in practice.
This chapter has not adequately explored higher order statistics of distributions of EJT.
These statistics have important implications for measuring reliability as one aspect of relative
service quality, and deserve further attention in future work.
On the London Overground
Aggregate EJT was found to vary substantially across the different London Overground lines
and across time periods of weekday service. Total EJT is greatest on the North London Line
in the AM and PM Peak periods, which also had among the highest estimates of mean
EJT. Passengers on this line during the peak periods suffer the most total EJT because
there are many more of them and because, on average, their journeys are the most delayed
relative to the timetable. The North London Line in the peak periods is, by this measure,
especially deserving of management and tactical planning attention. This is consistent with
155
PPM (i.e. OTP) results.
Further disaggregating EJT by direction, it was found that total and mean EJT on
the NLL in the AM Peak were substantially worse in the westbound direction (i.e. from
Stratford), driving the overall NLL AM Peak results. EJT was disaggregated again to the
level of individual scheduled services (in the westbound direction), where it was found that
total EJT was generally higher on those services with full 15 minute headways than on their
shorter headway leaders and followers.
Interchange passengers were found to have higher mean EJT than passengers on any
single line, particularly during the AM Peak. This is an indication that smaller delays on
individual lines lead to missed interchanges and thus longer delays for interchange passengers.
However, there are relatively few passengers interchanging between Overground lines, so the
total EJT attributed to them is small. The experience of interchange passengers is not
explicitly captured by PPM measurements.
The West London Line has mean EJT levels comparable to the North London Line,
despite having a substantially better PPM. The Gospel Oak to Barking Line is similar to
the other lines under both PPM and mean EJT. Line-level EJT results for the Watford DC
Line are not reliable because of the aforementioned problems with the assignment model.
Analyzing EJT for certain origin-destination flows on the WAT (those with little room for
assignment error) does indicate that this line has excessive running time between some of
its southernmost stations and Euston terminal.
EJT has the potential to be a useful input into the analytical tactical planning process,
as is explored in the following chapter. However, it is not possible to conclude at this point
that EJT is appropriate for use in contract or performance management on the Overground
or on other networks.
156
Chapter 9
Tactical Planning Case Study on the
London Overground
During the time that the research for this thesis was being conducted, London Overground
management researched, designed, and implemented a new tactical plan for AM and PM
Peak service on the North London Line. This chapter documents that tactical planning
intervention, which was influenced by some of the preliminary results of this thesis, and
evaluates its outcome in terms of certain aspects of service delivery and service quality.
This chapter is presented as a case study in that most of the work it describes was
conducted by other analysts and professionals. It depends heavily on in-person and e-mail
interviews with key Overground managers and on research conducted for those managers
by an industry consultant. The goal here is to illustrate how the methods developed in
this thesis for using automatic data can contribute to real-world tactical planning processes
considering a range of decision factors and variables. It is descriptive in nature, rather than
prescriptive.
Section 9.1 describes some aspects of the service plan, passenger demand, and operating
performance on the North London Line at the time of the tactical planning exercise. Section
9.2 describes how understanding of and relationships between these factors was synthesized
to guide the development of a revised tactical plan. Section 9.3 evaluates the outcomes of the
implementation of this plan using longitudinal before-and-after analysis. Section 9.4 draws
some conclusions regarding this evaluation, including its use of service delivery and service
quality measurements.
9.1
The North London Line: Spring 2008
This section describes some relevant information about the North London Line as of the
Spring of 2008, first in terms of the existing service plan, next in terms of passenger demand,
and last in terms of operating performance as expressed by different measures of service
delivery and service quality.
157
9.1.1
The Service Plan
The North London Line (NLL) is the backbone of the London Overground network. It serves
23 stations running 28 kilometers circumferentially around central London from Stratford in
the northeast to Richmond in the southwest. It connects to the Gospel Oak to Barking Line
(GOB) at Gospel Oak station (GPO) and to the Watford DC Line (WAT) and West London
Line (WLL) at Willesden Junction station (WIJ). Figure 9-1 schematically illustrates the
AM Peak service patterns and frequencies on the NLL (and other Overground lines) in Spring
2008.
Figure 9-2 uses a time-distance plot to show the published AM Peak timetable for the
NLL in Spring 2008.1 This plot shows a regular 15 minute headway (4tph) service making all
stops westbound from Stratford to Richmond and eastbound from Richmond to Stratford.
This regular service is augmented by occasional irregular additional services that split some
of the 15 minute headways into two smaller headways (of 7 and 8 minutes, 9 and 6 minutes,
etc). These irregular services include
• “Camden shuttles” that run approximately hourly between Stratford (SRA) and Camden Road (CMD) (departing Stratford at 07:59 and 09:31);
• “Clapham specials” that run approximately hourly between Stratford and Clapham
Junction (CLJ), diverting from the NLL to the WLL (not shown in plot) at Willesden
Junction (departing Stratford at 07:11 and 08:30);
• one full NLL service from Stratford to Richmond (RMD) at 09:02.
This timetable was developed before TfL and LOROL controlled the Overground network,
when it was a standard National Rail concession operated by the Silverlink TOC. David
Warner (2010), a planner in TfL London Rail, noted that the Camden shuttles were added
in 2004, and the Clapham shuttles in 2006. Oliver Bratton (2009), Head of Performance
and Planning for LOROL, noted that “TfL was getting concerned about the overcrowding
on the NLL (even though it was a DfT franchise). It therefore agreed to ‘buy’ additional
services from Silverlink for the peaks.” To add the additional trips, Silverlink planners “put
them into the existing schedule ... amongst the 15 minute service when appropriate.”
Describing the origins of this timetable, Warner (2010) noted that “the service was entirely driven by the rolling stock available, and the incremental nature in which additional
trains were added to the timetable. An overall view was not taken.” Bratton (2009) discussed
the timetable development process for the National Rail network more generally, noting that
“typically, a timetable evolves. As more and more trains run, the timetable tends to ossify,
becoming harder and harder to alter.” It appears from these comments that the highly
irregular NLL peak period timetable was in place largely as a historical artifact. It was not
the product of an analytical or data-driven tactical planning process.
1
Appendix A contains a list of station abbreviations.
158
WFJ
3t
ph
GPO
BKG
CMD
4 tph
SRA
0-1 tph
0-1 tph
WIJ
3 tph
EUS
North/West London Lines
Other London
Overground Lines
North/West London Line
Service Patterns
CLJ
2
tp
RMD
h
Figure 9-1: London Overground Spring 2008 AM Peak service patterns and frequencies
Distance
07:00
07:15
07:30
07:45
08:00
08:15
08:30
08:45
09:00
09:15
09:30
09:45
RMD
KWG
GUN
SAT
ACC
WIJ
KNR
BSP
BSY
WHD
FNY
HDH
GPO
KTW
CMD
CIR
HHY
CNN
DLK
HKC
HMN
HKW
SRA
10:00
RMD
KWG
GUN
SAT
ACC
WIJ
KNR
BSP
BSY
WHD
FNY
HDH
GPO
KTW
CMD
CIR
HHY
CNN
DLK
HKC
HMN
HKW
SRA
07:00
07:15
07:30
07:45
08:00
08:15
08:30
08:45
09:00
09:15
09:30
09:45
Time
Figure 9-2: North London Line Spring 2008 AM Peak timetable
159
10:00
9.1.2
Passenger Demand
NLL AM Peak Origin-Destination Matrix
Table 9-1 shows a segment-level2 AM Peak origin-destination (OD) matrix for the NLL.
It is a summary of the results of Chapter 5, which were estimated from passenger journey
data from the Oyster smartcard ticketing system, automatic entrance counts from selected
station gatelines, and manual on-board passenger counts.3 This matrix includes journeys
that interchange with the NLL, but it “clamps” those journeys to the point at which they
would make that interchange (i.e. at Gospel Oak or Willesden Junction).
Origin
Segment
NLLE
GPO∗
NLLC
WIJ∗
NLLW
Total
∗
Destination Segment
NLLE GPO∗ NLLC
9,309
369
1,848
158
356
1,362
268
778
524
83
465
687
63
678
12,040
783
4,125
WIJ∗
392
94
596
359
1,441
NLLW
517
145
1,019
808
1,234
3,723
Total
12,435
753
4,023
1,880
3,021
22,112
Cells highlighted in grey depend only on NLL service West of Willesden Junction
Includes flows interchanging between NLL and other Overground lines at these interchange stations.
Table 9-1: Segment level NLL AM Peak origin-destination matrix
Section 5.5 of Chapter 5 estimated that a total of 37,124 passengers use the London
Overground on an average weekday AM Peak period. The NLL OD matrix in Table 9-1
shows that 22,112, or 60%, of all AM Peak Overground passengers use the NLL for some
portion of their journey. The cells of Table 9-1 highlighted in grey indicate passenger flows
which use the NLL only between Willesden Junction and Richmond (RMD), inclusive. They
total 5,510 AM Peak passengers, or 25% of total NLL AM Peak patronage. In other words,
75% of all AM Peak NLL passengers use the NLL only between Stratford and Willesden
Junction, inclusive.
This OD matrix was estimated on data from Spring 2009, after the tactical planning
change described in this chapter was analyzed (but before it was implemented). It is included
here because (i) it is representative of the rough Oyster-only analysis that was conducted at
the time; (ii) the same OD estimation could have been conducted on 2008 data; (iii) such an
estimation would likely have produced very similar results for the Spring of 2008, especially
in terms of OD distributions; (iv) this chapter is intended to illustrate how the methods
developed in this thesis can be used in practice.
2
Appendix B describes the line and segment abbreviations used here.
As described in Chapter 5, the manual on-board counts are intended to be replaced with automatic
estimates from loadweigh data.
3
160
Aggregate Load Profiles (NLL AM Peak)
Figure 9-3 plots the aggregate load profile for the NLL (in each direction) as measured by
the manual on-board passenger counts that were used to estimate the above OD matrix. The
most salient observation to be drawn from these plots is that by far the largest aggregate
link loads on the NLL during the AM Peak are westbound between Stratford and Highbury
& Islington (HHY). The aggregate load starts at over 4,000 total passengers out of Stratford
and grows at each successive station, peaking at close to 6,000 total passengers between
Canonbury (CNN) and Highbury & Islington.
Westbound (SRA to RMD)
Eastbound (RMD to SRA)
Aggregate Link Load
6,000
5,000
4,000
3,000
2,000
1,000
SR
H A
KW
H
M
N
H
KC
D
L
C K
N
N
H
H
Y
C
I
C R
M
KT D
W
G
PO
H
D
H
FN
W Y
H
D
BS
Y
BS
KN P
R
W
I
AC J
C
SA
G T
U
KW N
R G
M
D
SR
H A
KW
H
M
N
H
KC
D
L
C K
N
N
H
H
Y
C
I
C R
M
KT D
W
G
PO
H
D
H
FN
W Y
H
D
BS
Y
BS
KN P
R
W
I
AC J
C
SA
G T
U
KW N
R G
M
D
0
Link
Figure 9-3: NLL AM Peak load profile
Passenger Incidence Behavior
Section 6.3.3 of Chapter 6 found that the temporal distribution of passenger demand on
the North London Line was much less timetable-dependent than on the other London Overground lines. That is, passenger incidence behavior was more random on the NLL and less
a function of the timetable. Figure 9-4 plots a small selection of the passenger incidence
results from Figure 6-4 illustrating the difference between the NLL and the GOB in terms of
the respective distributions of passenger incidence times (over a given headway) in the AM
Peak.
Section 6.3.3 also quantified the implications of these distributions in terms of their effects
on passenger waiting time (with respect to the timetable). It found that the dependence on
the timetable observed on the GOB in the AM Peak reduced waiting time (with respect to
the timetable) by 29% compared with purely random passenger incidence. On the NLL the
comparable reduction was only 7.2%.
161
Density of Passenger Incidence
NLL
0
0.25
0.5
GOB
0.75
1
0
0.25
0.5
0.75
1
Time Since Prior Attractive Departure (Normalized by Incidence Headway)
Figure 9-4: AM Peak passenger incidence on NLL and GOB
9.1.3
Operating Performance: Service Delivery and Quality
PPM
Service delivery on the London Overground network is currently characterized in terms of
PPM – the fraction of trips making all scheduled stops and arriving at their terminal no
more than 5 minutes late. Section 8.3.2 of the previous chapter presented PPM results for
the 52 weekdays from 31 March, 2008 through 10 June, 2008, inclusive. PPM for the NLL
over this range of dates was 83% for the AM Peak period and 89% for the whole weekday.
This was the worst of all of the Overground lines.
Running and Dwell Times
ACT, A British railway consultancy, was retained by LOROL to study operations on the
NLL (ACT, 2008). They used automatic train movement data from the network’s signaling
and control system to analyze running and dwell times4 from April, 2007 through March,
2008, inclusive. As TfL and LOROL took control of the Overground network in November
of 2007, this study included a period of substantial institutional and branding change on the
NLL. ACT’s observations most relevant to this chapter can be summarized as follows.
• Over the course of the study period, increases in terminal-to-terminal running times
were observed in the AM and PM Peak periods in both directions. The largest increase
of 4% was observed in the AM Peak in the westbound direction (i.e. from Stratford).
• For both directions in the peak periods, the 80th percentile running time is between the
running time in the timetable and the PPM threshold (i.e. timetable plus five minutes);
the 90th percentile running time is above the PPM threshold.
• At the 80th and 90th percentiles, the peak period running time westbound (i.e. from
Stratford) exceeds the peak period eastbound running time by just over two minutes.
4
Dwell time, the time at which a train is stopped at a station, can be thought of as the segment running
time between the arrival and departure at that station.
162
• Dwell times increased (by an unspecified amount) over the course of the study period,
especially during the peak periods.
• As measured during only the first quarter (i.e. January through March) of 2008, there
was substantial “dwell time loss” – station dwell times in excess of those specified in the
working timetables. Nine out of the top ten westbound (i.e. from Stratford) scheduled
services in terms of average dwell time loss were in the AM Peak period. Likewise,
nine out of the top ten eastbound (i.e. from Richmond) scheduled services in terms of
average dwell time loss were in the PM Peak period.
• The worst five westbound services had average dwell time losses of 311 - 459 seconds.
They are, in order of decreasing least dwell time loss, the 07:52, 08:06, 08:22, 07:37,
08:52 trains from Stratford. For these services, the largest single-station dwell time
loss was experienced at Canonbury, which is the station with the peak departing load
(as seen in Figure 9-3) on the NLL.
• A statistical correlation was found, for individual station stops by individual scheduled
services, between the length of the leading headway and the station dwell time.
From these observations, the consultants drew two important conclusions regarding service delivery on the NLL. Firstly, that running times in the timetable are insufficient, particularly for the AM and PM Peak periods. Secondly, that dwell times, and corresponding
dwell time losses, were driven by passenger demand. The consultants provided only this
analysis of current conditions and their conclusions as to what may have been causing those
conditions. They did not offer any explicit recommendations on what actions should be
taken to improve those conditions.
Train Congestion
Two types of train congestion5 were also observed on the London Overground network –
that between Overground trains, and that between Overground trains and freight trains
on the NLL. Bratton (2009) noted that “turning trains at Camden was causing congestion
on the network” between Overground services. This congestion has not been studied or
quantified directly, only reported anecdotally by Overground management and operational
staff. However, based on examination of the timetable in Figure 9-2, it is not hard to believe
that such congestion was occurring. The two Camden shuttles that depart Stratford at 07:59
and at 09:31 both arrive at Camden Road within a few minutes of an eastbound train from
Richmond. Under these circumstances, even slight deviations from schedule could cause
congestion and delays to the trains from Richmond, to the Camden shuttle on its return trip
to Stratford, or to the subsequent westbound train from Stratford.
It is of course also possible that the NLL suffered from additional types and instances of
train congestion, especially at other junctions and at terminals. Congestion between Overground trains at Camden Road and other locations could have been identified and studied in
further detail through the use of time-distance plots (as in Rahbee, 1999, 2006; Vescovacci,
5
Train congestion can also be considered an element of service delivery; it is simply the extension of
certain segment running times with a specific causal explanation.
163
2001; Lee, 2002, for the Boston and Chicago metros). Such plots can be generated from
automatic train movement data recorded by the Overground network’s signaling and control
systems (that were used to study running and dwell times), rather than from timetables as
in Figure 9-2.
The study by ACT (2008) also examined freight services running on the NLL. These
services join the NLL at one of several “boundary” junctions between the NLL and the
larger National Rail network, run on the NLL for some length, and depart the NLL at
another boundary. The boundaries most commonly used by freight services to join or depart
the NLL are, in descending order, at Stratford, west of Camden Road, west of Gospel Oak,
and east of Acton Central. ACT found that, between 06:00 and 23:00, over 55% of freight
services were more than 5 minutes late or early at their boundary with the NLL.
In the same study, ACT also used data from the National Rail train incident and delay
tracking system to assess the impact of non-punctual freight trains on passenger services.
Their findings indicated that freight trains joining the NLL with larger deviations from their
respective timetables had a larger chance of causing a delay to Overground NLL trains. Bratton (2009) reported anecdotally that “there was no ability to absorb late running freights”
during the shorter headways in the timetable.
Excess Journey Time
Excess journey time (EJT) for the NLL as of the Spring of 2008 was examined in detail in
Section 8.3 of the previous chapter. The relevant results can be summarized as follows.
• The NLL in the AM Peak had by far the most total EJT of any Overground line in
any time period, followed by the NLL in the PM Peak.
• In terms of mean EJT (i.e. after normalizing by number of passengers) the AM Peak
was the worst time period for the NLL.
• In terms of total and mean EJT, the NLL in the AM Peak had over twice the EJT in
the westbound direction (i.e. Stratford to Richmond) as in the eastbound direction.
• Total EJT was severely unbalanced among individual westbound AM Peak scheduled
services on the NLL. The five scheduled services with the highest total EJT were, in
descending order, the 08:22, 07:52, 07:07, 08:52, and 07:37 trains from Stratford. These
services had full 15 minute headways (at Stratford) and had substantially more total
EJT than their respective shorter-headway leaders and/or followers.
• Mean EJT on the NLL was somewhat linearly correlated with PPM. However, the
relationship was weaker in the AM Peak than for the whole day, and in the AM Peak
for lower PPM values.
164
9.2
Tactical Planning Intervention: The Case for Even
Intervals
This section synthesizes the results of the previous section to explain the thinking behind a
specific tactical planning intervention that was implemented on the NLL. It does so primarily
from the perspective of the London Overground manager who was the driving force behind
this change. This manager was influenced by the results of some of the early research from
this thesis, and used some of these results to make the case to his stakeholders.
Certain factors in the decision to implement this change, such as complete costs and
benefits, were not available for this case study. In addition, the manager’s perspective is
supplemented here by analysis drawn from the final results of this thesis. In that sense, the
case this section makes for the tactical planning change is not precisely the case that was
made in practice. Nevertheless, it provides a context in which to illustrate the value of the
methods developed in this thesis for using automatic data to support the tactical planning
of an urban railway.
Of the results and analyses discussed in the previous sections of this chapter, the key
points that influenced the tactical planning intervention on the NLL are as follows. They
are focused on the AM Peak period, in which, as of Spring 2008, the NLL had the most
problems with performance.
• NLL trains were routinely delayed en route, as reflected by running times substantially
in excess of the timetable and by low PPM on-time performance scores.
• Excessive dwell times were found to be a major cause of en route train delays. They
were particularly problematic for westbound services from Stratford, for those services
with full 15 minute scheduled leading headways, and at those stations with the highest
departing passenger loads.
• Evidence existed to support the judgment that these dwell times were primarily a
function of passenger volumes.
• Near-random passenger incidence behavior suggested an explanation for uneven passenger volumes and resultant uneven dwell times – when passengers arrive (even approximately) randomly, services with longer headways will serve proportionally more
passengers.
• The confluence of these analyses is confirmed by the corresponding EJT results:
– In the AM Peak, mean and total EJT were substantially higher for passengers
traveling westbound than for those traveling eastbound.
– Moreover, total EJT for passengers in the market for the services with full 15
minute leading headways was substantially higher than for the services with
shorter leading headways. This was a product of the volumes of passengers in
those markets and the average delay to each of those passengers.
– The set of scheduled services with the highest total EJT in the AM Peak was
nearly congruent with the set of services with the longest dwell times in the same
time period.
165
– These results also reflected the delays to any passengers who may have been
unable to board crowded trains.
• Additionally, there was congestion caused by the reversing of shuttle services from
Stratford at Camden Road and by freight trains arriving at the NLL off-schedule
during short headways in passenger service.
As described in Section 9.1.1, the typical approach to tactical planning on this network
was to update the timetable incrementally. It became evident that more drastic measures
were needed in this case. Specifically, that the timetable should be revised wholesale to
provide as even headways as possible. Under the circumstances, it was proposed to achieve
this by combining the NLL and WLL during the AM and PM Peak periods into an even 10
minute headway (6tph) service between Stratford and Willesden Junction. From Willesden,
alternating trains would go on the NLL to Richmond and the WLL to Clapham Junction.
This was referred to as the “3 + 3” service.
The core idea behind this strategy was to balance passenger volumes across trains, thus
reducing dwell times and train and passenger delays. It was expected that passenger volumes
would increase on some trains (i.e. those with longer headways than in the current plan) and
decrease on others (i.e. those with shorter headways). While the change was not expected
to materially affect the total volume of passengers, the outcome was expected to be positive
on balance. The reasons for this are twofold.
Firstly, dwell times have been found to have a non-linear relationship to passenger volumes (e.g. Wilson and Lin, 1993; Puong, 2000, which found dwell time to respond as the
square or cube of the number of standing passengers). This implies that, holding the total volume of passengers constant, the decreases in dwell times on trains losing passengers
(i.e. the existing 15 minute headway services) would be larger than the increases in dwell
times on trains gaining passengers (i.e. the shorter headway services). Consequently, overall
delays should decrease. While the managers of the Overground may not have been aware of
the literature and mathematical modeling of dwell time. It is likely that they were intuitively
aware of its dynamics.
Secondly, consistent with the hypothesis of unbalanced on-train loads, it was anecdotally
reported that some passengers were unable to board overcrowded trains were be left behind
on the platform. Under the new timetable, some trains would be more crowded than under
the existing timetable but still below capacity. Others would be less crowded and allow more
(or all) passengers to board. Passengers currently denied boarding by overcrowded trains
would thus benefit substantially while other passengers would benefit (from less crowded
trains) or suffer (on more crowded trains) to a lesser degree.
Additionally, with no change expected in the punctuality of freight services using the
NLL, the even interval strategy would minimize the chance that a freight service would have
to be fit in between two passenger services separated by only 6 or 7 minutes.
While the decision to move to the “3 + 3” service is presented retrospectively in a logical
and linear fashion, the strategy was in fact realized somewhat serendipitously. Bratton
(2009) described the process by saying that “although it wasn’t obvious at the time, the
only solution from the above was a regular interval service which ran for as long [i.e. far] as
possible.”
166
9.2.1
“3 + 3” Service on the North London Line
Headway Adjustment and Frequency Reallocation
The new tactical plan resulting from the above analysis was referred to as the “3 + 3”
service because it integrated the NLL and WLL into a single trunk-and-branch service for
the AM and PM Peak periods. It is effectively an even 20 minute headway (3tph) service
between Stratford and Richmond superimposed with an identically spaced service between
Stratford and Clapham Junction. The two services are offset by 10 minutes, yielding an even
10 minute headway (6tph) trunk service between Stratford and Willesden Junction.
Figure 9-5 illustrates the “3 + 3” service pattern schematically. Figure 9-6 uses a timedistance plot to show the corresponding published AM Peak timetable for the NLL. Table
9-2 summarizes the changes in the evenness and frequency 6 of service for each segment of
the NLL and WLL.7
Segment
Between
SRA ⇔ CMD
CMD ⇔ WIJ
WIJ ⇔ RMD
WIJ ⇔ CLJ
Spring 2008 Service (tph)
“3 + 3” Service (tph)
Core
Add’l
Total
Core
Add’l
Total
(even) (uneven)
(even) (uneven)
North London Line
4
1-2
5-6 uneven
6
6 even
4
0-1
4-5 uneven
6
6 even
4
4 even
3
0-1
3-4 uneven
West London Line
2
0-1
2-3 uneven
3
3 even
Table 9-2: NLL and WLL service under the Spring 2008 and the “3+3” tactical plans
The only part of the WLL and NLL to lose any service frequency under this reallocation
was the western end of the NLL between Willesden Junction and Richmond. One additional
shuttle trip over this segment was added for the entire peak period, but overall the headway
increased from 15 minutes to 20 minutes (4tph to 3tph). Not surprisingly, this was the
most contentious aspect of this plan. However, the OD matrix estimated in Chapter 5 and
summarized in Section 9.1.2 shows that only 25% of the NLL passengers using the NLL
in the AM Peak used this segment of the line. The “3 + 3” tactical plan thus reallocated
service such that more passengers gained service than lost it. In doing this, it was able to
establish a service pattern with even headways throughout the network that was easier for
customers and operators to understand, remember, and use.
Running Time Adjustment
In addition to the headway and frequency changes, timetable running times were also adjusted. Bratton (2009) described conventional practice in National Rail timetable develop60
For even service, headway (in minutes) is tph
.
7
The segments used here are slightly different than the segments used elsewhere in this thesis. These
segments are defined on the basis of service frequencies, whereas the other segments are defined based on
the location of interchange stations.
6
167
WFJ
3t
ph
GPO
BKG
CMD
3 tph
SRA
3 tph
WIJ
3 tph
EUS
North/West London Lines
Other London
Overground Lines
RMD
North/West London Line
Service Patterns
CLJ
0-1 tph
Figure 9-5: London Overground “3 + 3” service patterns and frequencies
Distance
07:00
07:15
07:30
07:45
08:00
08:15
08:30
08:45
09:00
09:15
09:30
09:45
RMD
KWG
GUN
SAT
ACC
WIJ
KNR
BSP
BSY
WHD
FNY
HDH
GPO
KTW
CMD
CIR
HHY
CNN
DLK
HKC
HMN
HKW
SRA
10:00
RMD
KWG
GUN
SAT
ACC
WIJ
KNR
BSP
BSY
WHD
FNY
HDH
GPO
KTW
CMD
CIR
HHY
CNN
DLK
HKC
HMN
HKW
SRA
07:00
07:15
07:30
07:45
08:00
08:15
08:30
08:45
09:00
09:15
09:30
09:45
10:00
Time
Services starting or ending at Willesden Junction (WIJ) on this diagram start from or continue on to
Clapham Junction over the West London Line
Figure 9-6: North London Line “3 + 3” timetable
168
ment being to add running time between the penultimate and final stations on a line. This
increases PPM scores (i.e. on-time performance) and increases the chance that a train will be
in place for the beginning of its next trip, but has little effect on the fidelity of the timetable
to actual operating conditions on most of the line.
In this case, Bratton (2009) stated that his goal in designing the new timetable was to
bring it into alignment with actual operations so that customers traveling anywhere on the
line would not be “late” at their destinations. He was motivated to approach timetable design
this way by the concepts exposed in the development of the Oyster-based EJT measure.
Specifically, that lateness can be defined at the level of passenger journeys or OD flows
rather than terminal-to-terminal train trips.
In the new timetable, the running time between Stratford and Camden Road was shortened by 1-2 minutes on the basis that evening the headways would drastically reduce dwell
times. The running time between Camden Road and Richmond was lengthened by 3-4
minutes to account for discrepancies found in the study by ACT (2008). Both changes were
effected through 1 minute adjustments en-route rather than in large blocks of time at the end
of the line or segment of the line. The total running time between Stratford and Richmond
was lengthened by approximately 3 minutes on average over the AM Peak period.
Costs
Bratton (2010) noted that the changes in service described here were for all intents and
purposes cost-neutral. The reallocation of service frequencies and adjustments in running
times were such that the “3 + 3” service could be operated at approximately the same costs
as the existing timetable. No new rolling stock was required and only two additional crew
members – conductors at an annual salary of £23 thousand each – were needed to fully staff
the new timetable.
9.3
Evaluation
“3 + 3” service went into effect on the NLL and WLL on Monday, 20 April, 2009. This
section evaluates the outcomes of this tactical planning intervention, primarily through longitudinal analysis of measures of service delivery and service quality. These measures are
taken for a period directly after the implementation, and compared to two periods before
the implementation – one directly before and one a year earlier. The goal of this evaluation
is to assess, to the degree possible, the causal effects on passengers and on the operation of
changing the tactical plan. However, despite the large amount of data available, any number
of uncontrolled factors may confound this analysis. Final conclusions on the effects of the
“3 + 3” plan will be a matter of judgment on the part of the reader.
Because this evaluation is of a major change to the timetable, it is important to evaluate
service quality in absolute as well as relative terms. Consequently, total observed journey
time (OJT) will be analyzed along with EJT. All else being equal, any change in OJT should
be reflected in an equal change in EJT. However, any adjustment to the timetable will break
this link.
Service delivery is evaluated primarily in terms of PPM (i.e. on-time performance) and
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dwell times, the latter of which was analyzed in a follow-up study by ACT (2009) (the same
consultancy whose analysis contributed to the formulation of the “3 + 3” plan). Interviews
with London Overground management are also considered.
This evaluation is focused on the NLL, and uses the GOB as a control since there were no
substantial changes to the GOB timetable over this period. The GOB is not a perfect control
in that it has different service and demand characteristics from the NLL, but it should be
subject to similar universal influences such as weather, overall economic conditions, etc. The
NLL is evaluated as a whole (including passengers in both directions) and also for the core
market passengers traveling between Stratford and Camden Road in the westbound direction
(i.e. towards Camden Road). This “NLL Core” market is analyzed separately because it is
the only section of the line for which there was only a change in the evenness of headways
in the peak hours and not a change in the overall frequency of service.
Unfortunately, Overground services were moved to a different platform at Stratford station on the same day that “3 + 3” service started. This new platform was substantially
further from the ticket gatelines than was the original platform (which was close to the station entrance). The additional walking time was measured by this author to be at least one
minute at a brisk pace. This has the potential to seriously confound a longitudinal analysis
of journey times measured by the Oyster system, so all journeys to or from Stratford are
excluded. This is far from ideal, since Stratford is one of the most heavily-used stations on
the NLL. The resulting loss of data is just over 50% for the core market and just under 25%
for the entire NLL. While these numbers are large, they do leave a substantial amount of
data remaining for analysis, so the losses are considered acceptable.
9.3.1
Evaluation Data
The following three study periods are analyzed to evaluate the effects of introducing “3 +
3” service. They are determined in part by data availability.
Af ter2009: Weekdays from 20 April through 15 May and 1 June through 5 June, 2009,
inclusive. This is 5 out of the first 7 weeks directly following the introduction of “3 +
3” service.
Bef ore2009: Weekdays from 2 March through 13 March, 2009. This is a period of two
weeks shortly before the introduction of “3 + 3” service.
Spring2008: Weekdays from 21 April through 16 May and 2 June through 6 June, 2008,
inclusive. These are the weeks in 2008 corresponding to the weeks in the Af ter2009
period.
Complete PPM and timetable data were available for these study periods. Observed
and excess journey times (i.e. OJT and EJT) are measured from Oyster journey data, the
volumes of which8 (after exclusion of journeys to or from Stratford) are shown in Table 9-3.
At first glance the numbers in this table indicate increasing weekly ridership. However, this
interpretation does not account for changes in the Oyster penetration rate among Overground
riders. An increasing penetration rate would result in increasing volumes of Oyster data
8
“Passengers” are unique passengers as indicated by unique Oyster card IDs
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despite static volumes of overall ridership. This evaluation does not explicitly analyze total
ridership on the Overground network or lines in question.
Study
Period
Spring2008
Bef ore2009
Af ter2009
Length
(weeks)
5
2
5
GOB
Journeys Pax.
30,505 6,566
13,428 4,351
34,408 9,248
NLL
Journeys
Pax.
133,030 28,222
51,862 16,573
136,655 36,738
NLL Core (SRA→CMD)
Journeys
Pax.
17,226
4,050
7,280
2,487
19,217
5,755
Table 9-3: Volumes of Oyster data in evaluation study periods
Line and segment running time analysis is drawn from the report by ACT (2009).9 Unfortunately, ACT reported on changes in median rather than mean dwell times. Median
values mask the effects of large outliers, which for a nonlinear phenomena such as dwell time
are expected to be quite important, so changes in dwell time are not directly analyzed here.
9.3.2
Evaluation Results
Table 9-4 shows PPM, EJT, and OJT results for the three network segments for the three
study periods. It shows the difference from Spring2008 to Bef ore2009 to indicate the
changes in performance between the time the tactical planning analysis was done and just
before “3 + 3” was implemented. It shows the difference from Bef ore2009 to Af ter2009
with the hope of isolating the effects of introducing the “3 + 3” service.
The differences in EJT and OJT were tested in a single-sided difference of means ttest. All differences on the NLL and NLL Core were statistically significant at the 1% level.
Differences on the GOB between Af ter2009 and Spring2008 were significant at the 5% level,
but between intermediate periods were not significant even at the 10% level.
Study Period
Spring2008
Bef ore2009
Af ter2009
Bef 09 − Spr08
Af t09 − Bef 09
Af t09 − Spr08
GOB
PPM (%) EJT
95.5 1.27
96.3 1.21
95.5 1.19
0.8 -0.06
-0.8 -0.02
0.0 -0.08
OJT
25.32
25.25
25.14
-0.07
-0.11
-0.18
NLL
PPM (%) EJT
85.9 2.77
79.7 2.29
92.4 1.68
-6.2 -0.48
12.7 -0.61
6.6 -1.09
OJT
26.50
25.69
25.51
-0.81
-0.18
-0.99
NLL
EJT
2.33
1.39
1.75
-0.94
0.36
-0.57
Core
OJT
17.97
17.42
17.06
-0.55
-0.36
-0.91
Table 9-4: PPM and passenger journey time results and comparisons for “3 + 3” implementation
9
ACT did not use exactly the same study periods for its analysis of train operations data as was used
for the analysis of PPM and Oyster journey time data. However, the periods are very similar – two weeks
in May 2008, two weeks in March 2009, and two weeks following the “3 + 3” introduction – so the results
are considered to be applicable here.
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On the GOB, the changes in all three measures were small – PPM fluctuated by 0.8%
and returned to its original value of 95.5%, while OJT and EJT decreased by 0.08 minutes
(6.3%) and 0.18 minutes (0.7%), respectively, between the initial and final study period.
It is not unexpected that OJT and EJT did not vary by the exact same amount. While
the changes to the GOB timetable were minor, OJT could be affected by slight shifts in
(i) passenger incidence behavior, since EJT is calculated against scheduled waiting time;
or (ii) the temporal distribution of ridership over the AM Peak, since running times in the
timetable do vary slightly over the AM Peak. This illustrates some of the factors that may
confound the longitudinal analysis for the NLL, if only to a small degree.
Interpretation: Changes on the NLL Before the “3 + 3” Introduction
On the NLL as a whole, changes may be observed in all the calculated measures. PPM
increased (i.e. worsened) between the Spring2008 and Bef ore2009 study periods by nearly
6 percentage points. ACT (2009) found that over this time average train journey time from
Stratford to Richmond increased by about 30 seconds.
OJT and EJT decreased (i.e. improved), by 0.81 minutes (3.1%) and 0.48 minutes (17.3%),
respectively, over the 9 months between the first two study periods. For the NLL Core passengers, OJT and EJT decreased by 0.55 minutes (3.1%) and 0.94 minutes (40.3%), respectively.
It is interesting to note in these cases that the changes in EJT and OJT, measures of relative
and absolute service quality, were directionally opposite of the changes in PPM,10 a measure
of service delivery.
It appears that there were substantial improvements to absolute and relative service
quality on the NLL as experienced by passengers before the implementation of the “3 + 3”
service (i.e. NLL over the 9 months between Spring2008 and Bef ore2009). Bratton (2010)
attributes this primarily to “higher performing Network Rail infrastructure.” The 2008
TfL Investment Programme (Transport for London, 2007b) indicates that £56.9 million of
infrastructure (i.e. track, switch, and signal) upgrades were planned during this period. Much
of this investment was in support of capacity on the NLL to an eventual 12tph. It is difficult
to separate these capacity upgrades from investments that would improve infrastructure
performance at the same level of throughput, but this figure indicates the intensity of the
work that was done.
Interpretation: “3 + 3” Effects on the NLL
For the NLL, the comparison between the Bef ore2009 and Af ter2009 study periods should
give the clearest insight into the direct effects of introducing the “3 + 3” service. PPM
increased by over 12 percentage points while the average running time from Stratford to
Richmond increased by just under 20 seconds. Unfortunately, ACT (2009) did not report on
the distributions of running times, so it is impossible to say how much the change in PPM
is a result of improved service delivery as compared to the more generous standard set by
lengthening the running time in the timetable. During this period, the average train running
time from Stratford to Camden Road decreased by 50 seconds.
10
Directionally in the sense of improvement or worsening, not in terms of the numeric sign of the delta.
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OJT decreased by an additional 0.18 minutes (0.7%) for the NLL as a whole and 0.36
minutes (2.1%) for the NLL Core, indicating improved passenger journey times. The changes
in EJT, like those in PPM, are more difficult to interpret. For the NLL Core, EJT worsened (i.e. increased away from zero) while PPM and OJT both improved. This is not a
surprise, as the running time between Stratford and Camden Road was shortened in the
new timetable. OJT decreased but the scheduled journey times (SJT) decreased even more,
so EJT increased. This illustrates one of the disadvantages of timetable-based measures of
service quality such as EJT, which is further discussed in the following chapter.
Given the substantial changes to the timetable, the effects of introducing “3 + 3” service
may best be judged in terms of absolute service quality. The decreases in OJT suggest that
the tactical planning intervention improved the experience of NLL passengers. The changes
in OJT are 22.2% and 65.4% of the changes observed on the NLL and NLL Core, respectively,
between the Spring2008 and Bef ore2009 study periods.
Figure 9-7 plots total EJT by scheduled service for westbound passenger journeys on the
NLL between Stratford and Willesden Junction in the Af ter2009 period. Comparing it to
Figure 8-9 (the same plot but for the Spring2008 period) shows a more even distribution
of EJT across scheduled services during the height of the peak period. For example, in
Af ter2009 the differences between the services with the highest total EJT (the 08:09 and
08:39 trains from Stratford) and their respective leaders and followers is smaller, even in
relative terms, than the same differences for the services with the highest EJT in Spring2008
(the 07:52 and 08:22 trains from Stratford).
800
Daily Mean Total EJT (min)
600
400
200
D
A/
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M
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0
Time of Departure
Figure 9-7: Total EJT by scheduled service, westbound, after “3 + 3” implementation
Because the timetable and headways changed between these two study periods, incidence
behavior was also examined. Plots similar to Figure 9-4 did not show any noticeable change
in overall incidence behavior. Mean scheduled waiting time (which is part of the scheduled
journey time against which EJT is measured) decreased by 0.1 minutes (6 seconds) on the
NLL Core and increased by approximately the same amount over the entire NLL. These
changes appear to be a function primarily of the changes to the timetable rather than
changes in incidence behavior (i.e. passengers becoming more or less attuned to the timetable
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as discussed in Section 7.4.3).
Abdul Salique (2010), a TfL contract manager who represents TfL in its relationship with
LOROL, was interviewed about the effects of introducing the “3 + 3” service. It should be
noted that it is his job to hold LOROL to their contractual responsibilities while considering
the experience of the Overground’s passengers to whom TfL is ultimately accountable. He
noted that “overall it is good for passengers... There has been a lot of good passenger benefit
to a greater number of passengers than those that have been disadvantaged” (i.e. those
traveling west of Willesden Junction). “It has also improved train performance and has
made the timetable more robust and easier to recover from... Overall I would say we could
move more people during the peaks when we were a bit constrained before.”
9.4
Conclusions
The analysis in this chapter indicates the following preliminary conclusions regarding the
recent tactical planning intervention and resulting “3 + 3” service on the NLL. Conclusions
regarding EJT and the use of automatic data in tactical planning in general are presented
in the following chapter.
• The timetable is, overall, more aligned with actual operating conditions (i.e. segment
and line running times). That said, the “3 + 3” timetable may have been too ambitious
in terms of decreasing running time between Stratford and Camden Road.
• The service plan and timetable are, on balance, more aligned with the experience and
needs of passengers and operators. Headways have been evened out to correspond with
the largely random incidence behavior of NLL passengers. The service patterns and
timetable itself are simpler and more uniform than before the change, making them
easier for passengers to understand and easier for operators to operate.
• Passenger journey times have improved. Decreases observed in the 9 months leading up
to the “3 + 3” implementation are felt by London Overground management to have
resulted from substantial infrastructure investment, maintenance, and management
efforts. Additional decreases observed directly after the implementation are felt to have
resulted from the change to the tactical plan. The latter improvements in passenger
journey times are comparable to, if smaller than, the former improvements – 20%
overall and 65% on the most heavily used segment from Stratford to Camden Road.
• The change to the “3 + 3” service was approximately cost-neutral. Whatever benefits
were reaped by this tactical planning intervention on the NLL came at the cost of only
two additional crew members and the analysis and planning effort required to see it
through.
The causal relationships in the penultimate conclusion, particularly with respect to the
effects of infrastructure investment, have not been rigorously analyzed. If (and only if) they
are to be believed, it raises the question of whether an approximately cost-neutral tactical
planning effort had comparable but smaller effects on passenger journey times as a substantial
investment program and 9 months worth of maintenance and management efforts. Even if
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this question were answered affirmatively, it is not to say that tactical planning is a substitute
for capital investment (which comes as the result of strategic planning). Rather, it would
illustrate that the potential benefits and cost effectiveness of improved tactical planning
using automatic data should not be overlooked in the overall management, investment, and
planning of an urban railway.
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176
Chapter 10
Final Remarks
This chapter presents final remarks regarding the research documented in this thesis. Section
10.1 summarizes and draws conclusions about the methodological and applied results of the
previous chapters. Section 10.2 presents some recommendations for the use of automatic
data by the London Overground and Section 10.3 suggests future research directions.
10.1
Summary and Conclusions
This section presents a summary and conclusions, first for the various analytical methods
developed and used in this thesis, and next for the use of automatic data in tactical planning.
It also outlines the specific methodological contributions of this thesis.
10.1.1
Analytical Methods
Loadweigh Calibration
Chapter 4 developed and applied a method for calibrating train loadweigh systems to measure
passenger loads on trains. It used a simple linear regression model to compare loadweigh
measurements with corresponding manual passenger counts so as to estimate the average
passenger weight and tare weight of the loadweigh system. It found that the manual passenger counts provided, collected by a pair of surveyors at each station, were generally of
insufficient quality to accurately calibrate loadweigh systems. The exception to this finding
was at terminal stations where conditions allowed surveyors to count more accurately than
at other stations in the network.
Analysis of the limited data set (from terminals only) suggested that the assumptions
of an average passenger weight of 80kg, a 95% confidence interval of ±20 passengers (per
train), and no tare weight, as recommended by an industry expert (Smale, 2010), are in
fact reasonable. The number of paired observations of loadweigh measurements and manual
counts taken at terminals was limited to only 49 out of the whole set of 1,253. The regression
on this limited set produced results very close to prior findings including the following.
• It estimated the average weight of passengers at 81.4kg, with high statistical significance. This is only 1.8% different from the recommended value of 80kg.
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• It estimated an error bound of 10.8kg. This is the upper bound of the standard
deviation of random error in passenger loads inferred from loadweigh data. Assuming
normally distributed random error, this amounts to a 95% confidence interval of ±21.2
passengers (per train), as compared to the recommended ±20 passengers.
• It estimated a relatively small overall tare weight of 328.6kg (4.0 passengers), but this
estimate is not statistically significant.
• When data was segmented by individual train unit, it estimated nearly equal average
passenger weights and similarly small and statistically insignificant tare weights for
each unit. That is, there is no evidence to suggest that the tare weight is other than
zero.
In terms of methodology, the linear regression model used in this chapter appears suitable
for comparing loadweigh data to manual passenger counts. Because the residuals in these
regressions were found to be of approximately constant variance, the method of ordinary
least squares is adequate to estimate this model.
OD Matrix Estimation
Chapter 5 developed and applied a method, tailored to the circumstances of the London
Overground, to estimate time period level origin-destination (OD) matrices from multiple
types of automatic data. It developed an assignment model as required by OD estimation
methods which integrate data on OD flows with counts of on-board passenger loads. It applied the assignment model to an OD estimation process using the Information Minimization
method of Van-Zuylen and Willumsen (1980) to estimate an OD matrix for the Overground
network for the AM Peak period. It validated the resulting estimate against boarding and
alighting counts, and compared this validation to a validation of the existing Overground
OD matrix estimated using from TfL’s regional transportation models and surveys.
The following conclusions were drawn.
• Link flows from loadweigh measurements and/or manual on-board link counts can be
combined, through a mathematical estimation process, with aggregate transactional
data from the Oyster smartcard ticketing system to estimate time period level OD
matrices for the Overground network.
• The overall accuracy of the OD estimate is improved by the addition of automatic
entry and/or exit totals from gatelines at stations exclusive to the Overground.
• Of the wide range of available mathematical models and methods for assignment and
OD estimation, a relatively simple approach is sufficient to use these data sources
to improve the accuracy and currency of OD matrices for the Overground network
compared with the existing OD matrix from the London Travel Demand Survey and
RailPlan regional model.
• The key outputs of the network assignment model, which does not account for congestion or capacity constraints, are relatively insensitive to most embedded assumptions
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regarding passenger path choice. Specifically, the choice for most passengers of whether
or not to use the Overground network does not change when most of the model’s assumptions are violated.
• The Information Minimization method for OD estimation from link flows and a seed
matrix is suitable to the problem faced by the Overground. It is simple to implement,
is conceptually very similar to the matrix estimation method used by the London
Underground, and has the very important feature that its results are not sensitive to
overall scaling of the seed matrix when total number of passengers (i.e. the sum of the
OD matrix) is not fixed.
• The OD estimation process developed here is insensitive to measurement error in the
loadweigh data under two conditions. First, that the measurement error is unbiased
and uncorrelated with the actual number of passengers, which has been found to be
the case in this and other work. Second, that there is a sufficient quantity of loadweigh
data (i.e. at least eight weeks) over which to estimate average loads.
• The OD estimation method developed here does not treat the seed matrix as a lower
bound on the estimated matrix, and some estimated OD flows are, unrealistically, lower
than their respective values in the Oyster seed matrix. This is not considered a serious
problem for this method in practice because it affected only a very small portion of the
OD flows and those it did affect were for the most part relatively small flows to begin
with.
Broadly speaking, it is concluded that the methodology developed here would represent an
improvement with respect to the Overground’s current practices, but that there remains
potential for further improvement (as discussed later in this chapter).
Passenger Incidence Behavior
Chapter 6 developed and applied a method to analyze passenger incidence (i.e. arrival) behavior at stations using AFC data. The variables by which incidence behavior was analayzed
are, for each individual passenger journey, the scheduled headway relevant to that journey
and the time between incidence and the next relevant scheduled departure (the “scheduled
waiting time”). The method infers these variables given each journey’s origin, destination,
and time of entry. It uses schedule-based assignment to account for the heterogeneity of services that are likely to be used by different passengers, even at a single location (e.g. trunkand-branch service). It was implemented using open standard timetable formats and free
software tools.
The following conclusions were drawn about the methodology itself.
• It can be used to study passenger incidence behavior using large samples of disaggregate
journey data from AFC systems such as the Oyster smartcard system. It is able to
efficiently process thousands or millions of such data records.
• It can, for each passenger journey, estimate the waiting time and headway (with respect to the timetable), two of the most important quantities for studying passenger
incidence, even under quite heterogeneous conditions.
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With respect to the London Overground, the following have been concluded from the
results of applying the method to relevant Oyster data.
• Passenger incidence behavior is heterogeneous across the Overground network and
across times of day, and that the differences are broadly reflective of what has been
found to date in the literature. Incidence appears to be substantially more random on
the North London Line (NLL) than on the other Overground lines.
• On the lines with timetable-dependent incidence behavior (i.e. other than the NLL),
passengers reduce their mean scheduled waiting time by over 3 minutes, or up to 30%,
during daytime hours compared with random incidence behavior. On the NLL, such
reductions are much smaller, in some cases nearly zero, in both relative and absolute
terms.
This work has not attempted to rigorously identify the causes of these difference. Hypotheses
drawn from existing literature on the subject and knowledge of the Overground network
include (i) shorter headways (i.e. higher frequencies) and (ii) less reliable service on the NLL
compared to other lines.
Service Quality Measurement from AFC Data
Chapter 7 explored the issue of service quality measurement using passenger journey times
as measured by AFC systems (e.g. Oyster). It developed a method to measure excess journey
time (EJT) – the difference between the observed journey time (OJT) and a journey time
standard derived from the published timetable. EJT thus defined is a measure of relative
service quality that strikes a useful balance between the passenger’s and operator’s perspectives. It has found lasting application at a number of large urban railways. Actual passenger
journey times can now be measured (rather than modeled) directly from automatic data
produced by AFC systems such as the Oyster smartcard.
The method developed here includes different models for how passengers set journey time
standards depending on whether they are aware of the timetable (and specific departure
times) or not, as implied by their incidence behavior. It estimates EJT through comparing
the actual arrival time at the destination with the scheduled value as determined by a
schedule-based assignment of each journey given its origin, destination, and incidence time.
This method was found, despite its dependence on specific train departure and arrival times,
to be, in aggregate, unbiased regardless of the randomness of passenger incidence. In this
sense it is a unified method in that it can be applied regardless of specific passenger incidence
behaviors, whereas most measures of service quality and relative service quality have made
the assumption of random incidence. This result was rigorously proven for a single rail line
without interchanges, but intuitively should hold for a rail network. This is a very useful
result in practice. It allows for the estimation of aggregate EJT from only AFC (e.g. Oyster
smartcard) data and published timetables in a simple unified manner, regardless of service
frequencies or passenger behavior that vary across the network or over time.
EJT for individual passenger journeys on a given service was found to range from negative (i.e. early) by up to one headway to positive (i.e. late) by substantially more than one
headway. A negative EJT for a single journey does not in and of itself represent a problem
180
or inconsistency in the measurement scheme. However, it is difficult to interpret EJT for
individual journeys, in part because of the ambiguity with respect to passengers’ incidence
behavior and implied journey time standards. Consequently, EJT is not a particularly useful
measure for analyzing individual passenger journeys.
Aggregate EJT, on the other hand, is a measure of relative service quality with clear
meaning. It expresses the average passenger’s experience in terms of total journey time compared to what the timetable would imply, for a wide range of passenger incidence behaviors.
Individual EJT measurements are easily aggregated both spatially and temporally. When
aggregated, EJT is by its very nature passenger-weighted. Different aggregation functions,
for example mean or sum, can be used to present different types of passenger orientation.
Both such aggregations capture certain information about the passenger’s experience that a
service delivery measure such as on-time performance (OTP) does not.
Three particular issues were identified with the interpretation of EJT. Firstly, when a
substantial proportion of passengers are incident shortly after a scheduled departure time
based on an expectation that trains regularly depart late, and their expectations are correct,
EJT can be net negative. This could occur despite the fact that passengers may arrive
at their destinations on time or late compared to the schedule for the train they may have
expected to take. Such a situation highlights the need to study passenger incidence behavior,
as in Chapter 6, before analyzing EJT. No evidence of this problem was found for EJT on
the London Overground network. Such could still occur in practice.
Secondly, changes to the timetable may result in changes in EJT even when no change
in service quality has been experienced by passengers. As timetable revision is one of the
most common tactical planning activities, this poses a particular problem for the use of EJT
in longitudinal evaluation of changes in service quality. Lastly, while changes in passenger
incidence behavior will not bias EJT results, neither will benefits that passengers capture
from such changes (i.e. by reducing waiting time) be reflected. This too may confound
longitudinal interpretation of EJT results, and underscores the need to study passenger
incidence independently of EJT.
It may be the case that EJT and other measures of relative service quality are useful
primarily as tools for cross-sectional analysis to inform, but not evaluate, tactical planning
changes. Further conclusions regarding the application of EJT to railway tactical planning
(and evaluations thereof) are discussed in the following section.
10.1.2
Applications of Automatic Data to Tactical Planning
The case study presented in Chapter 9, which used London Overground EJT results presented in Chapter 8, provided a rich example of the use of automatic data for tactical planning
on the North London Line (NLL) of the Overground network. The models, methods, and
results of the earlier chapters of this thesis contributed to both the development of the new
tactical plan for the NLL and to the evaluation of the implementation of that plan. The
effects of this implementation appear to have been positive on balance. This case study
thus demonstrates the applicability of automatic data generally, and the data and methods
developed in the thesis specifically, for tactical planning of an urban railway.
Various measures of service delivery and service quality, all generated from automatic
data sources, contributed to the tactical planning exercise that led to the “3 + 3” service.
181
In terms of service delivery, dwell times, running times, and on-time performance (i.e. PPM)
were analyzed using train signaling and control data. They indicated that running times
in operation were substantially longer than in the timetable, and that excess dwell time,
particularly on certain scheduled services and at certain locations, was one of the main causes
of increased running times. Even when tremendous amounts of information are available on
actual passenger journeys, traditional measures of service delivery were found still to be quite
useful in starting the tactical planning process.
Service quality was analyzed primarily in a relative sense in terms of excess journey time
(EJT) as measured using Oyster journey data and the published timetable. An aggregate
analysis of total EJT helped direct attention to the experience of passengers traveling westbound on NLL in the AM Peak period. A more disaggregate analysis of EJT identified those
scheduled services whose passenger markets suffered the longest journey times relative to
the timetable. The analysis of service quality in terms of EJT largely confirmed the analysis
of the various service delivery measures, particularly in terms of which scheduled services
suffered the worst performance (i.e. those with the longest scheduled headways). EJT was
found to add an element of the passenger’s perspective to the tactical planning process. It
can focus tactical planning attention to the segments of passengers who need it most, and
can support and enhance analyses that have been initiated from the operator’s perspective.
Two analyses of passenger demand also contributed to the tactical planning process.
Passenger incidence behavior on the NLL was analyzed using Oyster journey data and the
published timetable. It was found to be substantially more random than previously assumed,
contributing to the decision to move the NLL to an even headway service. The use of automatic data can provide key insights into passenger behavior, helping to challenge standing
assumptions and develop tactical plans better suited to passengers current behaviors.
Also analyzed was the origin-destination matrix of overall AM Peak passenger demand
on the Overground network, estimated from aggregate Oyster passenger volumes, automatic
gateline entry counts, and manual on-board passenger counts (which can and should be
replaced in the future by automatic loadweigh data). This OD matrix indicated that the
proposed reallocation of some service frequency away from the western end of the NLL
towards the eastern end would benefit more passengers than it would harm. This reflects a
common consideration in tactical planning which illustrates the need for a high quality OD
matrix in almost any analysis.
The confluence of these analyses contributed to the development, proposal, and implementation of the even headway “3 + 3” service on the NLL and West London Line (WLL)
in the AM and PM peak periods. The development of the timetable for this service was also
influenced by the key concept inherent in the idea of measuring EJT – that standards can be
set and lateness can be measured at the level of individual passenger journeys or OD flows.
This led the developers of the timetable to adjust running times throughout the length of
the NLL rather than only at the end of the line as was typical on the National Rail network.
In this sense, EJT can be a useful tool to help shift tactical planning practices that may be
less oriented towards the passenger’s perspective than is desired.
Service delivery and quality on the NLL were analyzed longitudinally to evaluate the
effects of introducing the “3 + 3” service on passengers and on the operation. Because the
timetable changed so drastically in the “3 + 3” implementation, an additional measure of
absolute service quality was included in the evaluation. Observed journey time (OJT) was
182
estimated using only Oyster journey data. This and other measures were analyzed before and
after the introduction of “3 + 3” service. PPM increased substantially and OJT decreased
(i.e. they both improved). EJT decreased by substantially more than OJT for the line as a
whole and in fact increased for the core portion of the line, which was the portion towards
which the “3 + 3” service was targeted.
These discrepancies were found to be because the “3 + 3” timetable had lengthened
running times over the whole line and shortened them over the core portion. This highlights
the relative nature of EJT, illustrating its value as a relative rather than absolute measure. EJT provides good information about how the passenger experience compares to the
timetable, but not necessarily a clear picture of how it has changed in an absolute sense. It is
thus similar to on-time performance, but measured for and weighted by individual passenger
journeys.
Consequently, it is concluded that measures of relative service quality are not sufficient
for evaluating the effects of tactical planning changes, particularly those that modify the
timetable. In general it may also be necessary to measure absolute service quality. That
said, relative service quality measures such as EJT can be useful for the type of cross-sectional
tactical planning analysis that was described in this case study. They can help identify and
prioritize problems and suggest solutions, but are not always appropriate for judging the full
effects of those solutions.
10.1.3
Methodological Contributions
The research in this thesis, while for the most part applied in nature, has produced two
methodological innovations. These were discussed above, but are highlighted here for their
contributions to the literature. These new methodologies, primarily useful for applying
automatic data to railway tactical planning, include the following.
• Estimation of key variables for studying passenger incidence behavior from AFC data
under heterogeneous service patterns. Previous studies of passenger incidence all selected places and times of observation (be it with manual or automatic data) to avoid
ambiguity with respect to the services to be used by waiting passengers (e.g. excluding
trunk stations on a line with multiple branches). They trivialized the measurement of
key variables by selecting stations served by only a single service pattern and, in some
cases, with a constant scheduled headway. The contribution of the method developed
and tested in Chapter 6 (i.e. Algorithm 6.1) is that it allows the study of passenger
incidence across a network using AFC data without these limitations.
• Unified estimation of aggregate EJT from AFC data under heterogeneous service patterns and passenger incidence behaviors. Existing methods for estimating EJT make
the assumption that passengers are randomly incident and thus should expect to wait
half the scheduled headway. These methods do not apply to passengers whose incidence is non-random and whose journey time standards depend on specific scheduled
train departure and arrival times. They also pose an implementation challenge under
heterogeneous service patterns where different passengers at the same location face
different headways in practice (e.g. at trunk stations on a line with multiple branches).
183
The contribution of the method developed in Chapter 7 is that it makes no such
assumption about passenger incidence behaviors at a given location or for a given
service but is nevertheless unbiased. It makes assumptions about how passengers set
their journey time standards given their incidence behavior (which are consistent with
assumptions in other methods for randomly incident passengers). However, it was
proven that the actual type of incidence behavior is irrelevant for measuring aggregate
EJT with data from AFC systems such as Oyster.
Both of these methods use schedule-based assignment which was implemented for this
thesis using open standard format public timetables and free and open source software tools.
These methods should be of value in future research as described in the following section.
10.2
Recommendations for Data Collection on the London Overground Network
The general recommendation stemming from this thesis is that the London Overground
should move as much as possible towards the use of automatic data to provide key tactical planning inputs and away from dependence on manual passenger counts and surveys.
Specifically, it should adopt the strategy proposed in Section 3.2 and summarized in Table
3-1 to both reduce the cost and improve the timeliness of key inputs such as train level
passenger loadings and time period level OD matrices. The key elements of this strategy are
the following.
Train loads on individual scheduled services should be estimated directly from loadweigh
data. Resources permitting, additional calibration should be conducted to estimate the
average passenger weight and tare weight (per train unit or fleet wide). An average
passenger weight of 80kg and a zero tare weight may be used in this estimation if no
further calibration is conducted.
Average loads (on a given service at a given location) should be estimated from multiple
loadweigh measurements in a given analysis period. The number of samples needed for
a given level of accuracy should be determined from further analysis of larger samples of
loadweigh data than were available for this thesis. It is likely that somewhere between
one and two weeks worth of data will be sufficient to estimate average load to within
±10 passengers at a 95% confidence level.
Origin-destination (OD) matrices should, as described in Chapter 5, be estimated at
the time period (e.g. AM Peak) level from the combination of different types of automatic data including the following.
• Seed matrices estimated from aggregate Oyster journey data. Each seed matrix
should be estimated by averaging daily Oyster data from a representative sample
of days (e.g. ten weekdays) in the period of interest (e.g. a fiscal quarter).
• Aggregate link flows, estimated from loadweigh data, indicating the daily average
number of passengers riding Overground services in each direction between each
184
pair of consecutive stations in the given time period. These aggregate link flows
should be estimated as the sum of link flows on individual scheduled services, as
described above. When loadweigh data are used in estimating OD matrices, as
many data as possible should be averaged to overcome the random measurement
error introduced by loadweigh systems.
• Aggregate station entry and/or exit totals, estimated from station gatelines, at
stations that are fully gated and served exclusively by the Overground. Like
Oyster seed matrices, these may be estimated from a representative sample of
days in the period of interest.
These data should be integrated using the assignment model developed in Chapter 5,
which depends on RODS the network representation used in the London Underground’s
OD estimation process. They should be reconciled (to estimate a complete OD matrix)
using the Information Minimization method.
Station boardings and alightings (at the time period level) should be estimated by assigning the estimated OD matrix to the Overground network (using the assignment
model developed for OD estimation).
Total daily trips on the Overground network (at the time period level) should be estimated as the sum of the estimated OD matrix (for that time period).
This strategy should be extended as the Overground network is expanded. For example,
with the opening of the East London Line (ELL), loadweigh data should be obtained from
trains serving the ELL and Oyster and gateline data should be obtained for ELL stations.
The RODS network representation should be extended to cover the ELL to support OD
matrix estimation (for the Underground and the Overground).
10.3
Future Research
The analysis and results of this thesis suggest a number of directions for future research.
Loadweigh Calibration
Additional research should be conducted into the nature and magnitude of the various sources
of error associated with passenger loads inferred from loadweigh data. The weakness of the
analysis in this thesis stems primarily from the low quality of the manual counts against
which loadweigh data were compared. To remedy this and other issues, the following are
recommended.
• More calibration-quality data should be gathered (be it platform-based surveyors at
terminals or from on-board surveyors en route) and paired with corresponding loadweigh data. The regression models from Chapter 4 should be used to re-estimate the
calibration parameters and the error bound.
185
• In addition, additional calibration-quality data should be used to explore variability
in the parameter estimates and error bound across different individual units of rolling
stock.
• As identified by Nielsen et al. (2008a), additional analysis should be conducted at
different times of year to assess the systematic variation in average passenger weights
correlated with seasons and weather. It is possible that such variation could be ignored
in practice, but this question should be explored.
Loadweigh calibration results will likely vary across different types of rolling stock. Different railways (including the London Overground) will incur different costs in the loadweigh
calibration process, depending on the required or desired accuracy of the results. Best practices should be developed for railways to make the appropriate cost/accuracy tradeoff for
their respective uses of loadweigh data.
OD Matrix Estimation
One specific aspect of the OD estimation methodology used in Chapter 5 of this thesis
merits further research. The constraint of the seed matrix as a lower bound on the final
OD estimate should be added to the Information Minimization formulation. It is trivial to
add this constraint to the formulation, but it may make the model much more difficult if
not impossible to solve efficiently. It is possible that a lagrangean analysis similar to that
developed by Van-Zuylen and Willumsen (1980) would yield an efficient algorithm as it has
for the existing formulation.
Other OD estimation methods, for example those based on generalized least squares, may
also be applicable to this type of problem. A benefit of these methods is that they allow for
the estimation to take into account the varying statistical quality of the inputs rather than
treating all measured link flows as deterministic constraints. These methods were not used
here because they appeared to be inapplicable when the seed matrix is estimated from only
a fraction of journeys, as is the case with Oyster data. The possibility of augmenting these
methods to overcome this issue should be explored.
The assignment model and OD estimation methodology used here both assume no congestion effects or capacity constraints in the network. This assumption was made primarily
as an engineering simplification, but was justified in part by the structure of the Overground
network. The London Underground and National Rail are known, by passengers and managers alike, to face serious congestion problems. Consequently, OD estimation over the entire
network of railways in London using similar data would need to account for congestion and
capacity. A host of models and methods, some discussed in Chapter 5, have been developed
(by other authors) to treat these issues. They should be applied and tested on London’s
networks, both for the sake of exploring those models and methods and in support of the
planning and management of London’s railways.
Passenger Incidence Behavior
The method developed Chapter 6, which builds heavily on some of the basic concepts of
schedule-based assignment, should be used to support further study of passenger incidence
186
behavior. The work of Bowman and Turnquist (1981) has been influential in shaping the
understanding of the relationships between headway, reliability, passenger behavior, and
waiting time. Their work should be updated and extended using the method of this chapter
to cheaply and easily gather large samples of passenger data across heterogeneous networks.
Their work also depends on measurements of service reliability, which should be gathered
from automatic vehicle tracking systems.
With such rich data available at such low cost, the study of passenger incidence should be
disaggregated to understand the range and consistency of behavior of individual passengers,
for example as by Csikos and Currie (2008). Moreover, longitudinal analysis should be
conducted to understand the aggregate and disaggregate behavioral responses to changes in
key service variables such as headway and reliability.
The London Overground network represents an ideal opportunity to conduct such a
study – its passengers can clearly be studied via Oyster data, and its trains are tracked by
a computerized signaling system. Once the East London Line opens, the network will have
headways ranging from 5 to 30 minutes during most hours of the day. As the network grows
and headways and reliability levels change, the evolution of passenger incidence behavior
should be studied over time to understand passengers’ reactions to such changes.
Nearly three decades have passed since the work of Bowman and Turnquist (1981). In
that time, many strides have been made towards informing passengers in real time about the
status of public transport services. Such information is now often distributed via in-station
signs and announcements as well as over the internet to passengers’ computers and, more
importantly, mobile devices outside of stations. It is crucial to advance the understanding
of passenger incidence to include the effects of real-time information. This requires careful
thinking and research designs, but should be able to take advantage of the methodology
developed here.
Service Quality Measurement from AFC Data
The unified estimator developed in Chapter 7 for mean EJT with respect to the published
timetable should be further analyzed. While it was found to be unbiased for journeys on
a single rail under a range of circumstance, the following additional areas of analysis were
identified.
• Interchange journeys – the estimator should be rigorously analyzed for journeys on a
railway network with interchanges.
• Reliability – estimators for other higher-order statistics of the EJT distribution, which
indicate reliability rather than average performance levels, should be proposed and
analyzed. One difficulty in this analysis is that, even with all journey time standards set
based on the published timetable, the distribution of EJT depends on how passengers
are incident and set their standards whereas mean EJT does not.
The research by this and other authors on using data from AFC systems (e.g. Oyster) to
measure absolute and relative service quality has only scratched the surface of understanding
the complete passenger experience. For example, the research by Chan (2007), Wilson et al.
(2008), and Uniman (2009) have developed measures of reliability based on assumptions
187
about how randomly incident passengers set standards given their previous travel experiences. This work analyzed EJT (i.e. mean performance, not reliability) using standards set
based on the timetable for a range of passenger incidence behaviors; it was found however
to be confounded by certain types of experience-based incidence behavior. Hopefully, these
different threads can be synthesized to develop measures of relative and absolute service
quality, in terms of mean performance as well as reliability, for all types of passengers with
any type of incidence behavior or journey time standards.
Further research should be conducted on the application of the results of this thesis
and related work towards the management and planning of urban railways. For example,
while the focus of this thesis was on tactical planning, there may be opportunities to apply
service quality measurements towards performance and contract management. These tasks
have different requirements from tactical planning in that they are more highly structured
activities, often with financial stakes. While EJT may not be appropriate for such uses,
primarily because of its sensitivity to changes in the timetable and to certain exceptional
passenger incidence behaviors, other AFC-based measures of service quality, such as total
journey time or reliability buffer time, may be applicable.
188
Appendix A
London Overground Station
Information and Abbreviations
Table A-1 shows information for each station on the London Overground network, including
presence of ticket gatelines and availability of interchanges to the London Underground (LU)
and National Rail (NR) networks. NLC is the National Location Code. Lines and segments
are defined in Appendix B.
Table A-1: London Overground stations
Station Name
Acton Central
Blackhorse Road
Barking
Bushey
Brondesbury Park
Brondesbury
Caledonian Road & Barnsbury
Clapham Junction
Camden Road
Canonbury
Carpenders Park
Crouch Hill
Dalston Kingsland
London Euston
Finchley Road & Frognal
Gospel Oak
Gunnersbury
Hampstead Heath
Headstone Lane
Harlesden
Highbury & Islington
Hackney Central
Code
ACC
BHO
BKG
BSH
BSP
BSY
CIR
CLJ
CMD
CNN
CPK
CRH
DLK
EUS
FNY
GPO
GUN
HDH
HDL
HDN
HHY
HKC
NLC
1404
522
514
1395
1438
1437
1439
5595
1440
1441
1442
7406
1429
1444
1445
1409
591
1413
1434
596
603
6977
189
Line
NLL
GOB
GOB
WAT
NLL
NLL
NLL
WLL
NLL
NLL
WAT
GOB
NLL
WAT
NLL
INT
NLL
NLL
WAT
WAT
NLL
NLL
Segment
NLLW
GOB
GOB
WATN
NLLC
NLLC
NLLE
WLL
NLLE
NLLE
WATN
GOB
NLLE
WATS
NLLC
INT
NLLW
NLLC
WATN
WATC
NLLE
NLLE
Gated
Yes
Yes
Yes
No
No
Yes
No
Yes
Yes
Yes
No
No
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Interchange
LU
NR
No
No
Yes
No
Yes
Yes
No
Yes
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
No
No
Yes
No
No
No
No
No
Yes
No
Yes
Yes
No
No
Hackney Wick
Homerton
Harrow & Wealdstone
Harringay Grn Lns
Hatch End
Kilburn High Road
Kensal Green
Kensal Rise
Kenton
Kensington Olympia
Kentish Town West
Kew Gardens
Leyton Midland Road
Leytonstone H Rd
North Wembley
Queens Park London
Richmond
South Acton
Stonebridge Park
South Hampstead
South Kenton
Shepherds Bush
Stratford
South Tottenham
Upper Holloway
West Brompton
Watford High Street
Watford Junction
Woodgrange Park
West Hampstead
Willesden Junction
Wembley Central
Walthamstow Queens Rd
Wanstead Park
HKW
HMN
HRW
HRY
HTE
KBN
KNL
KNR
KNT
KPA
KTW
KWG
LEM
LER
NWB
QPW
RMD
SAT
SBP
SOH
SOK
SPB
SRA
STO
UHL
WBP
WFH
WFJ
WGR
WHD
WIJ
WMB
WMW
WNP
6978
6979
597
7401
1398
1415
617
1448
620
3092
1449
621
7402
7403
659
680
686
1452
717
1451
709
9587
719
7404
1524
755
1455
1402
7467
1421
766
751
7407
7408
190
NLL
NLL
WAT
GOB
WAT
WAT
WAT
NLL
WAT
WLL
NLL
NLL
GOB
GOB
WAT
WAT
NLL
NLL
WAT
WAT
WAT
WLL
NLL
GOB
GOB
WLL
WAT
WAT
GOB
NLL
INT
WAT
GOB
GOB
NLLE
NLLE
WATC
GOB
WATN
WATS
WATC
NLLC
WATC
WLL
NLLE
NLLW
GOB
GOB
WATC
WATC
NLLW
NLLW
WATC
WATS
WATC
WLL
NLLE
GOB
GOB
WLL
WATN
WATN
GOB
NLLC
INT
WATC
GOB
GOB
No
Yes
Yes
No
No
No
Yes
No
Yes
No
No
Yes
No
No
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
No
No
No
Yes
No
No
No
Yes
No
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
No
No
Yes
No
No
No
No
Yes
Yes
No
No
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
No
Yes
Yes
No
No
Yes
No
Yes
No
No
No
Yes
No
No
Appendix B
London Overground Line and
Segment Abbreviations
The existing London Overground network can be divided up into lines and line segments as
described in Table B-1. Note that the two interchange stations that lie on multiple lines,
Gospel Oak and Willesden Junction, are considered separately. There are other stations
on the network with interchanges to other networks (i.e. National Rail and London Underground) but these are the only two with interchanges between different London Overground
services.
Line Segment
NLL
NLLE
NLLC
NLLW
WLL
WAT
WATN
WATC
WATS
GOB
INT
Description
North London Line, Stratford ⇔ Richmond
NLL East, Stratford ⇔ Kentish Town West
NLL Central, Hampstead Heath ⇔ Kensal Rise
NLL West, Acton Central ⇔ Richmond
West London Line, Clapham Junction ⇔ Willesden Junction
Watford DC Line, Watford Junction ⇔ Euston
WAT North, Watford Junction ⇔ Headstone Lane
WAT Central, Harrow & Wealdstone ⇔ Queens Park
WAT South, Kilburn High Road ⇔ Euston
Gospel Oak to Barking Line, Gospel Oak ⇔ Barking
London Overground interchange stations (Gospel Oak, Willesden Jn)
Table B-1: London Overground lines and line segments
191
192
Appendix C
Schematic Map of TfL Rail Services
The image in Figure C-1 on the following page shows a schematic map of TfL rail services,
including the London Underground, London Overground (with the new East London Line),
and the Docklands Light Railway. The map also illustrates the 9 fare zones from which rail
fares in London are determined.
193
A
B
C
D
Chesham
Amersham
Uxbridge
1
9
Chalfont &
Lat imer
8
Chorleywood
Wat ford
Croxley
2
7
Pinner
Nort hwood
Nort hwood
Hills
Moor Park
Ruislip
Manor
Wat ford Junct ion
Wat ford High St reet
3
West Brompt on
3
4
Brent Cross
Hendon Cent ral
Colindale
Burnt Oak
Edgware
8 7 6
St anmore
Canons Park
Queensbury
Kingsbury
Golders Green
5
4
3
5
Mill Hill East
Gospel
Oak
High Barnet
6
Tot t eridge & Whet st one
Woodside Park
West Finchley
Crouch Hill
Finchley Cent ral
East Finchley
Highgat e
Archway
Tufnell Park
Sout hgat e
Arnos Grove
Bounds Green
Wood Green
Turnpike Lane
Epping
Debden
7
Lought on
Theydon Bois
Cockfost ers
Snaresbrook
Sout h Woodford
Woodford
Blackhorse
Road
Walt hamst ow
Queen’s Road
Leyt onst one
Pudding
Mill Lane
St rat ford
Leyt on
Leyt on
Midland Road
3
Walt hamst ow
Cent ral
Sout h Tot t enham
Homert on
Mile End
East
India
8
Roding
Valley
Grange
Hill
6
9
Upminst er
Upminst er Bridge
4
Elm Park
Hornchurch
Dagenham
East
Dagenham
Heat hway
Becont ree
Upney
5
Barkingside
Fairlop
Hainault
Chigwell
4
Newbury Park
Gant s
Hill
Redbridge
Wanst ead
Leyt onst one
High Road
Wanst ead Park
Woodgrange Park
Barking
Cyprus
Beckt on
Gallions Reach
Woolwich Arsenal
8
9
St at ion in Zone 8
St at ion in Zone 9
9
St at ion in Zone 2
St at ion in bot h zones
St at ion in Zone 1
St at ion in Zone 4
St at ion in bot h zones
St at ion in Zone 3
St at ion in Zone 5
St at ion in Zone 6
St at ion in Zone 7
St at ion in bot h zones
1
2
3
4
5
6
7
Explanat ion of zones
4
King George V
Beckt on Park
Royal Albert
Prince Regent
Cust om House for ExCeL
3
East Ham
Royal
Vict oria
Plaist ow
Upt on Park
West Ham
Canning
Town
3
London Cit y Airport
Pont oon Dock
West Silvert own
Nort h
Greenwich
8
Airport
Tramlink
Riverboat services
Nat ional Rail
St ep-free access from t he
plat form t o t he st reet
Int erchange st at ions
Blackfriars St at ion closed
Key t o symbols
Lewisham
Elverson Road
Dept ford Bridge
Greenwich
Cut t y Sark for
Marit ime Greenwich
2
West
India Quay
Poplar
Blackwall
All Saint s
Langdon Park
Devons Road
Bromleyby-Bow
Bow Road
Hackney
Wick
Hackney Cent ral
Dalst on Kingsland
2
Bet hnal
Green
Bow Church
St epney Green
2
West ferry
Whit echapel
Shadwell
Limehouse
Wapping
Canary Wharf
Heron Quays
Sout h Quay
Mudchut e
Crossharbour
Island Gardens
New Cross
7
Buckhurst Hill
Oakwood
Haggerst on
Hoxt on
Shoredit ch
High St reet
Aldgat e
East
Tower
Gat eway
Rot herhit he
Tot t enham
Hale
Harringay
Green Lanes
Seven
Sist ers
Canonbury
Finsbury
Park
Aldgat e
Dalst on Junct ion
Highbury &
Islingt on
Manor House
Arsenal
Old St reet
Moorgat e
1
Tower
Hill
Fenchurch St reet
Monument
River Thames
Canada
Wat er
5
Int erchange st at ions
Locat ion of Airport
Riverboat Services
Bus Service
Vict oria
Wat erloo & Cit y
DLR
London Overground
Surrey Quays
Bermondsey
New Cross Gat e
London
Bridge
Liverpool
St reet
Upper Holloway
Caledonian Road
Angel
Caledonian
Road &
Barnsbury
Holloway Road
Kent ish Town
Camden
Road
Chancery
Lane
Bank
St . Paul’s
Barbican
Farringdon
King’s Cross
St . Pancras
Kent ish
Town West
Hampst ead
Heat h
Chalk Farm
Camden Town
Eust on
Square
Russell
Square
Holborn
Covent Garden
Cannon St reet
Mansion House
Leicest er Square
Morningt on
Crescent
Eust on
Goodge
St reet
Warren St reet
Great
Port land
St reet
2
Belsize Park
Hampst ead
Finchley Road
& Frognal
West Hampst ead
Kilburn
Willesden Green
Dollis Hill
Neasden
Brondesbury
Park
Oxford
Circus
Green Park
Piccadilly
Circus
Borough
Blackfriars
Temple
Embankment
Sout hwark
Lambet h
Nort h
Brixt on
6
Bakerloo
Cent ral
Circle
Dist rict
Hammersmit h
& Cit y
Jubilee
Met ropolit an
Nort hern
Piccadilly
Key t o TfL lines
Elephant & Cast le
Kenningt on
5
St ockwell
Oval
2
1
Wat erloo
West minst er
St . James’s
Park
Charing
Cross
Tot t enham
Court Road
Regent ’s Park
Baker
St reet
St . John’s Wood
Swiss Cot t age
Finchley Road
Edgware
Marylebone
Road
Sout h
Hampst ead
Brondesbury
Kilburn
High Road
Bond
St reet
Marble
Arch
1
Lancast er
Gat e
Edgware
Road
Bayswat er
Not t ing
Hill Gat e
Queensway
High St reet
Kensingt on
Hyde Park Corner
Vict oria
Pimlico
Sloane
Square
Knight sbridge
Gloucest er
Road
Sout h
Kensingt on
Imperial
Wharf
Vauxhall
Clapham
Junct ion
4
3
Clapham Nort h
Clapham Common
Clapham Sout h
Balham
Toot ing Bec
Toot ing Broadway
Colliers Wood
4
Source: Transport for London (2010d)
Morden
Sout h Wimbledon
Earl’s
Court
Holland
Park
Wimbledon
Wimbledon Park
Sout hfields
East Put ney
Put ney Bridge
Parsons Green
Fulham Broadway
2
West
Kensingt on
Barons
Court
Kensingt on
(Olympia)
2
Shepherd’s
Bush
Lat imer Road
Ladbroke Grove
Paddingt on
Queen’s Park
Kensal Green
Kensal
Rise
Wembley
Park
Prest on
Road
Kent on
Special fares apply
Bushey
Carpenders Park
Hat ch End
Headst one Lane
Harrow &
Wealdst one
Nort hwick
Park
Sout h Kent on
Whit e
Cit y
West bourne Park
East
Act on
Wood Lane
Hammersmit h
Goldhawk Road
Shepherd’s Bush
Market
Nort h
Act on
Royal Oak
Kilburn Park
Maida Vale
Warwick Avenue
Willesden Junct ion
Harlesden
St onebridge Park
Wembley Cent ral
Nort h Wembley
Harrowon-t he-Hill
Nort h Harrow
West
Harrow
West
Act on
Act on Cent ral
Gunnersbury
Kew Gardens
Richmond
3
Turnham St amford Ravenscourt
Brook
Park
Green
Sout h Act on
Chiswick
Park
2
4
Act on Town
East cot e
Sudbury Hill
Sout h Harrow
Rayners Lane
Ruislip
Rickmanswort h
West Ruislip
Hillingdon
Ickenham
Ruislip
Gardens
Sout h Ruislip
Alpert on
Sudbury Town
Perivale
Nort h Ealing
Park Royal
Hanger Lane
3
5
Hounslow Cent ral
Hounslow East
Ost erley
Bost on Manor
Nort hfields
Sout h Ealing
Ealing Common
Ealing Broadway
Greenford
Nort holt
5 4
Hounslow
West
Hat t on Cross
Heat hrow
Heat hrow
Terminal 4
6
Heat hrow Terminal 5
E Terminals 1, 2, 3
F
Transport for London 04.2010
1
Figure C-1: Schematic map of TfL rail services
A
B
C
D
E
F
194
Appendix D
Assignment Model Algorithm for
Operator Aggregation
This appendix provides additional detail on implementing the operator clamping aggregation
described in Section 5.3.1. The most subtle part of this computation is that of finding the
inner (clamped) OD flow for a given path for a given outer (unclamped) OD flow. The
complex part of this computation is illustrated the below excerpt from the ODNet program
developed to implement the assignment model of Chapter 5.
The excerpt shows the declaration of a Clamp class (in the Java programming language);
an object of this class would be created for each possible path for each outer OD flow.
After creating this object, the links in the given path would be examined in order. For
each boarding link, the board method would be called; for each alighting link, the alight
method. At the end of such a process, the ods member of the Clamp object would contain
a list of all of the inner clamp probabilities – the fraction of the outer OD flow assigned to
each inner OD flow.
public class Clamp {
String opCode;
HashMap<String,Double> ods = new HashMap<String,Double>();
AlightLink prevAlight = null;
List<ClampEntry> clamps = new ArrayList<ClampEntry>();
double currShare = 0;
// Start with the "operator code" of the
// operator for which the clamp is being computed
public Clamp(String opCode) {
this.opCode = opCode;
}
public void board(BoardLink bl) {
// the service link which the boarding link connects to
ServiceLink sl = bl.getServiceLink();
195
// with interavailability, the given operator may only provide some
// share of the total frequency in this combined service link
double freq = sl.getOperatorFrequency(opCode);
double share = 0;
if(freq != 0) {
share = freq/sl.getFrequency();
}
if(share < currShare) {
clampTo(prevAlight, share);
}
else if(share > currShare) {
ods.put(bl.getStationID(), share);
currShare = share;
}
}
public void alight(AlightLink al) {
prevAlight = al;
}
public void finish() {
if(prevAlight != null) {
clampTo(prevAlight, 0);
}
}
private void clampTo(AlightLink al, double share) {
if(share < currShare) {
double throughShare = share/currShare;
if(throughShare < epsilon) {
throughShare = 0;
}
double alightShare = (1 - throughShare);
Set<String> os = new HashSet<String>(ods.keySet());
for(String o : os) {
String d = al.getStationID();
double oShare = ods.get(o);
ClampEntry ce = new ClampEntry(o,d,oShare * alightShare);
clamps.add(ce);
196
double newShare = throughShare * oShare;
if(newShare < epsilon) {
ods.remove(o);
} else {
ods.put(o, newShare);
}
currShare = share;
}
}
}
private class ClampEntry {
String o;
String d;
double share;
public ClampEntry(String o, String d, double share) {
super();
this.o = o;
this.d = d;
this.share = share;
}
}
}
197
198
Appendix E
Terms and Abbreviations
This appendix lists and defines a number of the terms and abbreviations used in this thesis. It does
not include abbreviations for specific London Overground stations, lines, or line segments; these
are described in Appendices A and B.
AFC: Automatic Fare Collection.
DLR: Docklands Light Railway.
EJT: Excess Journey Time; the difference between a passenger’s OJT and SJT.
ELLX: East London Line eXtension; the project to rebuild and extend the old East London Line
as part of the London Overground network.
GLA: Greater London Authority; the governing body for the greater London area.
Headway: The time between two successive public transport services.
Interavailable: Refers to services with identical stopping patterns on a given corridor.
JTM: Journey Time Metric; the name of the scheme by which the London Underground measures
EJT.
LO: London Overground.
LOROL: London Overground Rail Operations, Ltd; the private concessionaire with operating
responsibility for London Overground services.
LU: London Underground.
MIT: Massachusetts Institute of Technology.
NLRIP: North London Railway Infrastructure Project; an investment project to improve capacity
and reliability on the London Overground network.
NR: National Rail.
OD: Origin-destination.
OJT: Observed Journey Time; the observed duration of a passenger journey, for example as measured by AFC data.
OLS: Ordinary Least Squares; a method by which to estimate mathematical models such as linear
regressions.
OSI: Out-of-Station Interchange; a no-cost interchange on the London railway network that involves exiting and re-entering the system.
OTP: On-Time Performance; the fraction of trains arriving some timepoint within some threshold
from the scheduled time.
199
OXNR: Oyster eXtension to National Rail; the project to extend the Oyster system to National
Rail network in London.
Oyster: The smartcard ticketing system for London’s public transport network.
Pax: Passengers.
PAYG: Pay as You Go; the fare class of passengers who pay for individual journeys using a stored
value on their Oyster card.
PPM: Public Performance Measure; the name of the scheme by which OTP is measured on the
UK National Rail network.
RODS: Rolling Origin-Destination Survey; the process by which OD matrices are estimated for
the London Underground.
SJT: Scheduled Journey Time; the scheduled duration of a passenger journey as derived from
published timetables.
TfL: Transport for London; the municipal transport authority for the London.
Timepoint: A location at which public transport service arrivals, passings, or departures are
timed.
TOC: Train Operating Company; a private concessionaire, such as LOROL, with operating responsibility for a National Rail franchise.
200
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